Tubing Design Concept

The uncertainties regarding actual loading conditions and the state of the tubing
(e.g., corrosion, anomalies due to poor handling) considerably exceed our
analytical capabilities to determine the resultant stresses. The tendency in the oil
industry therefore has been not to be overly sophisticated in analyzing an
extremely complex system, but rather to make designs on the basis of a set of
idealized loading conditions that have proven adequate in the past, such as those
presented in Table 1. It is important to remember that each company has its
own philosophy, criteria, and design factors to consider. The balance of design
assumptions versus actual conditions is depicted in Figure 1 (The balance of
design assumptions versus actual conditions).

Figure 1

While this may lead to a tendency to overdesign, the relative cost of the convenience
is generally fairly small. Extreme caution should therefore be used in making
modifications to the idealized loading assumptions. For special, severe loading
conditions (e.g., ultra deep >20,000 ft (6000 m), very high pressure >10,000 psi (70
MPa), very hot >300° F (150° C)), it is necessary to make a detailed computer-
assisted stress analysis.
Condition Loading Design Typical Design Factor
Criteria

Burst Internal Kill pressure 1.125

on
hydrocarbon-
filled tubing

External Packer fluid

and zero
annulus
pressure

Considerations Check effects

of
compression

Collapse External Casing head 1.125

pressure=
shut-in tubing
pressure

Internal Tubing empty

and
depressured

Considerations Check effects

of tension

Tension Running Buoyant Body: 1.333

weight in
completion
fluid

Joint: 1.8*

Tension and Operating Cold Body: 1.125

Compression stimulation
and hot
production
conditions

Joint: 1.333

Considerations Check effects

of
temperature
and pressure
changes

Total Stress Triaxial Max. stress 80% yield

*Assuming separate checks are not planned on shock and bending effects;
otherwise use 1.5.

Table 1: Typical criteria for tubing design on a flowing well

In many field situations and preliminary estimates, to establish the weight and
strength of the tubing it is sufficient simply to look at the tubing rating and to
apply the corporate design factor. However, it must be recognized that loading
conditions vary over the length of the tubing string, and to properly visualize this
it is generally advantageous to carry out a graphical tubing string design.

Graphical Tubing String Design

This is a convenient way of understanding loading conditions and presenting

design results. The technique is presented in Example 2 (part 1) and illustrated in
Figure 2 (Graphic tubing design estimated operating pressures),

Figure 2

Figure 3 (Graphic tubing design burst loads), and Figure 4 (Graphic tubing design
tubing selection).
 Figure 3

Abbreviations are presented in the Nomenclature.

 Figure 4

Example 2 (part 1)

Graphical Tubing Design

Planning Data

KBE: 3000 ft (915 m)

TD: 11,500 ft (3500 m)

Tbg: 2 7/8 in. OD (73 mm)

Closed-in bottomhole 5500 psi (38 MPa)

pressure:

estimated from mud weight

Formation breakdown 12,500 psi (86 MPa)

pressure:

estimated from offset well

Fracture propagation 9200 psi (63 MPa)
pressure:

estimated from offset well

Packer fluid: inhibited oil (0.38 psi/ft)

Production: expect sour gas

(gas gravity = 0.80 — reservoir)

(gas gravity = 0.70 — separator)

J55 or L80 tubular to be used

Stimulation: fracture expected (assume 20 barrels per minute);

maximum allowable annulus pressure is 2000 psi (13,790
kPa)

THP Estimate

Depth of Gas Gravity

Hole

(ft) (m) 0.60 0.65 0.70 0.80

1000 305 .979 .978 .976 .973

2000 610 .959 .956 .953 .946

3000 915 .939 .935 .930 .920

4000 1219 .920 .914 .907 .895

5000 1524 .901 .893 .885 .870

6000 1830 .883 .873 .854 .847

7000 2133 .864 .854 .844 .823

8000 2438 .847 .835 .823 .801

9000 2743 .829 .816 .804 .779

10,000 3048 .812 .798 .764 .758

11,000 3353 .795 .780 .766 .737

12,000 3660 .779 .763 .747 .717

13,000 3962 .763 .746 .729 .697

14,000 4267 .747 .729 .712 .678

15,000 4572 .732 .713 .695 .659

16,000 4876 .717 .697 .670 .641

17,000 5181 .702 .682 .652 .624

18,000 5486 .687 .656 .645 .607

19,000 5791 .673 .652 .631 .590

20,000 6097 .659 .637 .615 .574

Table 2: Ratio between surface pressure and bottomhole pressure in gas wells
for a range of gas gravities

At a gas gravity = 0.8, CITHP = 0.727 CIBHP = 3999 psi

At a gas gravity = 0.7, CITHP = 0.757 CIBHP = 4164 psi

For a kill situation:

bottomhole injection pressure = CIBHP + 2000 psi = 5500 psi + 2000 psi =
7500 psi

If gas gravity = 0.8, THIP = 0.727 BHIP = (0.727) (7500)

=5453 psi

Assumed Fracture Conditions

1. Formation breakdown achieved with water

2. Fracture job carried out with water-base fluid

Friction loss in 2 7/8 in. tubing at 20 BPM using water with friction reducer is 350 psi/1000 ft
for 11,500 ft (Dowell Handbook)
FPP = 9200 psi

Friction = +4025 psi (350 11.5)

Head = -5175psi (0.45 11,500)

Frac THP= 8050 psi

Prepare a depth pressure plot ( Figure 2 ) in the following manner:

1. Plot the closed-in bottomhole pressure (CIBHP).

2. Plot the formation breakdown pressure (FBP) and the fracture

propagation pressure (FPP).

3. Plot the packer fluid gradient, fracture fluid gradient, and water
gradient.

4. Estimate wet and dry gas gradients and plot these up from the
closed-in bottomhole pressure.

5. Establish the closed-in tubing head pressure for normal

production conditions (i.e., oil or, as in this case, wet gas) and for
worst case design assumption (usually dry gas).
 6. Establish maximum THP for which completion is to be designed,
which normally will be kill or stimulation conditions (fluid gradient
through FBP, FPP, or specified differential above CITHP). For
Example 2, the graphical design should now look like Figure 2 .

7. Establish through inspection the greatest differential pressure at

surface and downhole (usually stimulation conditions). Determine
what steps can be taken to reduce loading (e.g., maintaining
maximum allowable annulus pressure during stimulation). Plot
adjusted annulus pressure line ( Figure 3 ).

8. Plot burst load line (BLL) as difference between most critical

tubing and annulus pressures. The BLL is a function of the relative
densities in the tubing and annulus. BLL will generally, but not
always, decrease with depth ( Figure 3 ).

9. Plot critical collapse load conditions (CLL). Normally we assume

that a slow leak has changed the CHP to CITHP and that tubing is
empty and depressured. This can occur in gas wells if the tubing
becomes plugged or a downhole safety valve is closed. Conditions
can approach this situation in oil wells after a fracture treatment if
operators commence kickoff before bleeding off annulus pressure.
(In some cases this may be a more critical load ( Figure 4 ).)

10. Plot pressure test conditions (PT). This is often the most critical
load to which a completion is subjected. Consider timing of the
pressure test and density of fluids in the tubing and annulus at time
of test.

11. Look up tubing performance data in API Bulletin 5C2.

12. Adjust API internal yield (burst) and collapse resistance

specifications with design factor (see Figure 1 and API Bulletin
5C2).

13. List resulting tubing capabilities ( Figure 4 ).

14. Compare design loads with tubing capabilities and select

tubing. In most cases the optimum tubing grade and weight will
vary with depth. To minimize costs and/or tensional loads, such
variations may be incorporated, although there will then be a
constraint on pressure-testing capabilities. However, most
operators prefer to use a common weight and grade throughout the
completion, if possible. This reduces the risk of installation and
operating errors. When regulations permit, the designer may be
able to compromise slightly on accommodating loading conditions
deep in the hole, if the associated design assumption is extremely
unrealistic (e.g., a completely empty tubing in a high productivity
oil well). However, the designer must first check on how critical the
actual biaxial (or triaxial) loading conditions are likely to be and
make appropriate notes in the well file.

With reference to Example 2, in Figure 4 the options include the following:

1. full string of 6.4 lb/ft L80 tubing
 2. 0 to 6500 ft = 6.4 lb/ft J55
6500 to TD = 6.4 lb/ft L80

3. full string of 6.4 lb/ft J55 with modified collapse design criteria of
2000 psi as maximum CHP with an empty tubing

Since 2000 psi is the maximum allowable annulus pressure during stimulation, option 3 may
be an acceptable design. Since the differential cost of J55 and L80 is around $3 per ft, the
potential saving of $34,500 between options 1 and 3 may justify further detailed engineering
work. On the other hand, if the wellstream is expected to be extremely corrosive, the higher
grade tubing may be selected in any case to provide a corrosion allowance.

The key things to note from Figure 5 (Effect of buoyancy on axial load) are

the most severe burst loadings occur at surface

Figure 5

the most severe burst and collapse loadings occur during pressure
testing, well kill, and stimulation

the most severe collapse loading occurs downhole

additional annulus pressure can be used to reduce burst loading,

provided the casing is strong enough
 the tubing-head pressure during kill operations (THIP) often
approximates or exceeds the reservoir pressure (CIBHP)

With relatively small tubing strings (<3.5 in. or 90 mm), the inherent burst and collapse
strength is so high that some engineers do not bother with tubing design in wells with depths
of less than 8000 ft (2500 m), unless overpressures are expected.

Simplified Tensional Strength Design

Although burst and collapse resistance may not be significant considerations in

pumping wells, tensional strength is a critical design parameter for all wells.
Coupling leakage and failure, which accounts for 80% of the problems in well
tubulars, often may be the result of inadequate tensional design rather than a
burst or sealing problem. In this respect, it is particularly important to remember
that test pressures impose substantial piston forces on the tubing (e.g., a 2000
psi (13.8 MPa) pressure test on a plug set inside 2 7/8-in. (73-mm) tubing will
increase the tension on the hanger by (2000)( /4)(2.44l)2 = 9360 lb (42 kN).

It is also important to recognize that, unlike other strength parameters, the API
joint strength is based on a failure condition rather than the onset of plastic
deformation. The failure condition is either an unzipping of the pin and box in the
case of API threads, because of yielding (also called "jump-out"); or breakage of
reduced cross section at the threads in the case of square threads.

Finally, there are all sorts of additional tensional loads that we do not normally
analyze in detail (e.g., shock loading and drag forces during running, bending
stresses, buckling, cross-sectional piston forces, changes in buoyancy).

Since it is common practice to make a preliminary tensional design using tubing

weight loading only, a higher design factor is used for tension and especially for
joint strength (Table 1, above). Some companies and more conservative
engineers will even ignore the potential benefits of buoyancy. Buoyancy results in
a piston force on the lower end of the tubing and as a first approximation it may
normally be assumed that

(12)
where:
WB = buoyant weight

WN = weight in air

= density of steel (± 8 gm/cc)

= density of fluid

Figure 5 graphically depicts the tensional and compressional forces at work on a tapered
string of tubular goods. The load resulting from the weight of the pipe is shown for a string
weighed in air, and with the buoyant forces accounted for as piston forces or approximated
using Equation 12. We can see that at a point approximately midway in the length of the
heavier pipe at the bottom of the string there is a change from compression to tension. This is
also the concept which guides the design of drillstrings with the purpose of keeping the
drillpipe in tension while using the heavier drill collars to maintain a compressional load on the
bit.

Part 2 of Example 2 gives the preliminary tension design considerations for the
completion already covered in part 1.

Example 2 (part 2)

Preliminary Tension Design

Tubing weight: 6.4 lb/ft

Tubing length: 11,500 ft

Packer fluid: inhibited oil

0.38 psi/ft = 0.88 gm/cc

WN = 6.4 11,500
= 73,600 lb

= 0.89 73,600

= 65,504 lb

Joint Specifications

J55 L80

EUE HYD CS EUE HYD A95

API joint 99.7 100 135.9 128

strength (Klb)

Design factor 1.8 1.8 1.8 1.8

(Table 1)

Design capacity 55.4 55.6 75.5 71.1

(Klb)
Tubing Tension Design Considerations
1. Requires L80 tubing at surface

2. Requires joint strength capability of EUE or equivalent

3. In view of pressures, depth, and H2S would probably select

premium grade coupling

Many companies have these design techniques programmed for the computer and use the
same general technique for both tubing and casing designs.

Tubing Design Parameters

It is important to remember that while the primary function of the tubing is as a

conduit for hydrocarbon production or for injection of water or gas, the most
severe loadings often occur during well service or killing operations, or during
pressure tests. It is therefore prudent to make provision for these operations
when designing a completion, and to check out the tubing limitations when
planning a well servicing operation (e.g., a stimulation or a workover) . Care
must be taken not to increase completion costs excessively by trying to make
provisions for all sorts of unlikely, but possible, occurrences. It must also be
remembered that there are steps that can be taken to mitigate the induced
stresses during many operations (e.g., applying annular pressure or heating
fracturing fluids). On the other hand, the consequential costs of a failed tubing
string, or of having to run a special working string, in terms of deferred
production and rig time, can be quite substantial. Assessment of the most cost
effective solution is generally a judgment call based on the engineer's experience
and on corporate attitudes and policy. A typical set of parameters has already
been illustrated in Example 2.

Burst

The tubing and wellhead should be designed for squeeze and kill conditions. Since
fines in the perforations or oil can sometimes cause a "check valve" effect when
attempting to squeeze back liquids, many completion designers like to have the
flexibility of being able to raise the bottomhole pressure to the FBP or at least to
the FPP. However, with high permeability reservoirs or gas wells in which fracture
stimulation is unlikely, completion engineers are often satisfied with a certain
minimum differential for injection. The value selected varies from area to area
and from company to company, but is commonly either around 1000 psi (7 MPa),
or 33% of the reservoir pressure. The author suggests

1. FBP where k1 < 100 md

kg < 50 md

2. FPP for squeezing liquids, where k1 > 100 md

3. CIBHP + 1000 psi (7 MPa) for squeezing gas, where

kg > 50 md; or for squeezing liquids, where k1 > 1000 md

From the rock mechanics theory presented by Geertsma (1978) and others it may be
deduced that in a tectonically relaxed area, a provisional estimate of the fracture propagation
gradient (FPG) can be obtained from the equation

(13)

FPG < FBG < 1.1 psi/ft (25 kPa/m) (14)

where:
sv = overburden stress ( ~1 psi/ft depth)

p = pore pressure, psi

D = depth, ft

FPG = formation propagation gradient, psi/ft

FBG = formation breakdown gradient, psi/ft

The specification of the pressure test conditions is often critical to burst design. Government
regulations sometimes specify pressure test conditions (e.g., to at least 90% of the reservoir
pressure or to 1000 psi (5 MPa) over the maximum differential pressure expected at the
packer). If no regulations exist, most operators test to their tubing design conditions.

Collapse

Severe collapse loads on the tubing can occur

in gas wells and high GOR oil wells with low-flowing bottom-hole pressures and
deep-set safety valves, after blowdown to test a plug, etc.

during annulus pressure tests, or operation of shear circulation devices

where there are pressured annuli

during underbalance perforating or testing at high drawdown

during tubing blowouts

It is important to remember that tension reduces collapse strength. This biaxial effect should
be examined for large diameter tubings, especially if reduced collapse design assumptions
and/or a deep-set safety valve is used.

Tension

Tubing strings are not only subjected to running tensions with all the associated
shock and acceleration loadings, but also to varying operating stresses due to
piston forces on the steel and/or any plugs, pumps, standing valves, and the like
in the tubing. Moreover, if the tubing is anchored or held by a packer, its
operating tension will vary as a result of

thermal effects (hot production or cold kill fluid)

piston effects (changes in buoyancy and forces at joint upsets)

ballooning effects (changes in internal or external pressure)

buckling effects (longitudinal instability)

These potential problems are listed in terms of their most common relative magnitude
(although the relative importance of piston and ballooning effects is variable).

Combined Loading

While the designer of tubular goods normally talks in terms of burst, collapse, and
tension compression as if they were independent, it is obvious that in most actual
loading situations they occur simultaneously. Precise stress analysis should really
consider a triaxial loading situation.

The simultaneous solution of all the associated equations is rather complicated. A

number of computer programs are available, but for most field engineers they will
be a "black box" solution. This can be dangerous. It is important to check that the
formulas are properly handled, particularly with respect to collapse, which is a
"stability effect." Therefore it is usual for critical stress analyses (e.g., for ultra
deep, high pressure, or sour wells) to be undertaken by a specialist consultant,
research group, or intracompany task force. Moreover, since this is not the
routine design technique, design factors are less well proven (although a value of
1.25 is often used).

A more convenient approach for the intermediate range, moderately complex

design problem is to use the ellipse of biaxial yield stress proposed by Holmquist
and Nadai (1939). The critical relationships are (a) tension reduces collapse
resistance; (b) compression reduces burst resistance.

The other important concept in the consideration of triaxial loads is that pressure
changes affect axial stresses or cause tubing movement. This has been
extensively discussed in SPE papers by Lubinski (1962), Hammerlindl (1977), and
Stillebroer (1967).

Bending

Bending stresses can be significant in large tubulars. They are compressive in the
inner wall and tensional in the outer wall, the most detrimental being

(15)
where:
R = the radius of curvature (ft)

sb = bending stress

E = Young's modulus (for steel, E = 30 106 psi)

do = outside diameter of the tubular

Bending stresses result from both hole curvature and buckling. The effects of doglegs need
only be considered if they are very severe (>10°/100 ft; 10°/30 m) or if very large tubing (5 1/2
to 7 in.; 140 to 178 mm) is being used.