Tubing:

The tubing is the flow string through which the produced oil and gas move from the reservoir

to the surface handling facilities. In addition to the produced fluids, the tubing may be

required to control pressures and fluids during stimulation or squeeze conditions. Poor tubing

designs may result in tubing failure, which necessitates expensive remedial operations.

The typical production system contains the tubing, a packer, the seal assembly, and several

flow control devices.

Tubing Design Criteria

The three major tubular systems (casing, tubing, and the drillstring) used in drilling are

designed with different criteria. Casing is typically designed for burst, collapse, and tension,

whereas the drillstring is designed for collapse and tension, with burst seldom playing any

important role. Likewise, tubing is designed with a completely different set of guidelines.

Failure to recognize the differences may result in an under designed string.

Stress is the controlling factor in tubing design. Later examples will show that tubing

designed for stress considerations is overdesigned for burst, collapse, and tension. Stress and

tensile loading are different parameters and, as such, should not be confused or misused in

the tubing design, as is often done.

Factors Affecting Stress:

Tubing lying on the pipe rack does not encounter any significant, externally imposed stresses.

After it is placed in the well, it must withstand stresses from many sources. A knowledge of

these stress sources and the manner in which they affect the pipe is necessary to select pipe

capable of withstanding the expected loads.

Tubing hanging in the well must withstand the load of its own weight. This factor can be

significant in deep wells. Fig. 1 shows a stress graph for 6.4-lb/ft tubing hanging in a 10,000-

ft well that contains no packer fluids.

Wells without packer fluids, as described in Fig. 13-2, are seldom used in high pressure areas.

The common case is a tubing string hanging in a fluid with equivalent fluid densities inside

and outside of the tubing.

Fig: 1 Tubing stresses in a well with no fluids

Fig. 2 shows the same tubing string stress (Fig. 1), but the string is hung in a 9.0-lb/gal packer

fluid. The stress factors in this case are the tubing weight and the hydrostatic pressure of the

packer fluid acting on the horizontal cross-sectional area of the tubing at the bottom of the

string.

Fig: 2 Tubing stresses in a well with 9.0-lb/gal fluid

Temperature has an impact on tubing stress. Cooling normally causes pipe contractions

(shortening), and heating results in elongation. The normal expected length change is

0.0000069 in. per inch of tubing for each degree Fahrenheit change in temperature. If the

tubing is prevented from moving, as is common with some production packer systems,

stresses build in the tubing.

Ballooning, or radial pressure and fluid flow, results from internal and external pressures

causing the tubing to bulge, or balloon, outward (or inward). The ballooning changes the total

length of tubing (Fig. 3). As with temperature, packer systems that inhibit the expected tubing

movement increase tubing stress.

Buckling is the formation of helical spirals in the tubing string (Fig. 4). The depth above

which buckling does not occur is the neutral point of buckling, which should not be confused

with the neutral point in a tension- compression analysis. Buckling forces and the tubing-

casing geometries affect the severity of the buckling or its pitch.

Bending stresses result from buckling. As the pipe is strained from the flexing, stresses are

changed in the grain structures of the pipe wall. As the pipe bends, the outer wall lengthens

and the inner wall shortens. Therefore, stress changes will be different for each case. Fig. 5

shows the expected results.

Fig: 3 ballooning shorten the tubing

Fig: 4 Tubing buckling

Fig: 5 Bending stresses

Packer and Seal Arrangements

The packer and seal assembly provides the pressure integrity between the producing

formations and the tubing. Unfortunately, this equipment also limits tubing movement, which

results in stress increases. Various types and combinations of packer systems are currently

used.

The completion type affects the stresses in the tubing. A single completion has a bottom

packer. Multiple completions normally use additional packers that restrict vertical and

buckling tubing movement. Gravel pack completions are similar to single completions with

respect to tubing stress.

Packers

A packer is a device that seals the tubing-casing annulus and forces produced fluids into the

tubing. The exterior of the packer contains slips to prevent packer movement and a sealing

element. The slips are rated for tensile loading and should be evaluated when the packer is

selected.

The sealing rubber is typically a nitrile compound with 60-70 durometer hardness. High

formation temperatures may necessitate the use of harder rubbers (80-90 hardness). In

addition, K-Ryte @ (Dupont) or equivalent sealing elements must be used in sour gas

environments when certain corrosion inhibitors are used.

The size of the packer bore is an important variable in buckling calculations. It is seldom the

same size as the tubing outer diameter.

Seal Assembly

The seal assembly attaches to the bottom of the tubing and provides the pressure seal between

the tubing and the packer. The standard seal assembly contains two 1-ft seal units. The

locator assembly allows upward tubing movement and prevents downward movement when

the locator is set on the packer. The anchored assembly screws into the packer and prevents

any vertical movement.

Producing Conditions Affecting Tubing Design

Tubing design must be evaluated for the producing conditions it is expected to withstand. In

general, these conditions are as follows:

space-out

flowing

stimulation/squeeze

depletion

The severity of the stress loads under these operating conditions controls the tubing selection.

Seven items must be known for each of the conditions before the stresses can be computed:

packer fluid density

tubing fluid density

annulus surface pressure

tubing surface pressure

surface tubing temperature

bottom tubing temperature

tubing friction pressure

Tubing fluid density is easily established for oil or salt water. However, gas densities in terms

of lb/gal are usually assumed to be in the range of 1-2.5 lb/gal. Wet gases may be heavier.

This value should be examined closely if flowing conditions are more severe than the other

operating conditions.

The tubing friction pressure can be difficult to estimate. However, the worst stress case

occurs when the friction pressures are zero. The design approach presented in this section

will assume that these pressures are negligible.

Space-out. The space-out condition occurs when the tubing is positioned as desired relative

to the packer and the production tree. The usual conditions are that

1) the fluid density is the same for the annulus as the tubing,

2) no pressure exists at the top of the tubing and casing, and

3) some weight (10,000- 30,000 lb) is set on the packer.

The temperature at the bottom of the tubing is approximately equal to formation temperature.

Flowing. Oil and gas movement up the tubing causes several stress changes for various

reasons. The maximum tubing pressure (SITP) is greater than at space-out conditions. In

addition, the overall tubing temperature is increased. A satisfactory method of comparing

temperature changes is to evaluate the average of top and bottom temperatures at flowing

conditions.

Stimulation/Squeeze. These conditions are often the most severe that tubing must withstand

during its life. Although these conditions may exist for a relatively short period, they must be

included in the design considerations.

The typical considerations are 1) high tubing pressures and fluid densities, 2) annular backup

pressure, and 3) cooling effects due to surface fluids being pumped down the tubing. Fluids

used during these conditions include cement and acid.

Depletion. Depletion conditions occur when the formation pressures are reduced to a non

economical productive level. Depletion-like circumstances occur when the perforations are

plugged or the tubing is blocked with sand or other obstructions. The tubing pressure is low

or zero and the temperatures are approximately equal to the original space-out values.

A typical set of values for all operational conditions is shown in Table 1.

Space-out Flowing Stimulation/Squeeze Depletion

Packer fluid density, lb/gal 9 9 9 9

Tubing fluid density, lb/gal 9 6 16.4 6

Surface annulus pressure, psi 0 0 1000 0

Surface tubing pressure, psi 0 2800 4500 0

Surface tubing temperature, F 70 145 45 70

Bottom tubing temperature, F 240 240 110 240

Friction pressure gradient, psi/ft 0 0 0 0

Table 1: Typical Operating Conditions

Stress Evaluation:

Grade selection for the tubing string is dependent on the determination of the stresses. The

calculation procedures for the stresses must be completed in the following order:

1. force determinations

2. tubing length changes

3. stresses resulting from tubing length changes

This approach will be followed in this section.

Sign

Item Positive (+) Negative (-)

Force Compression Tension

Length changes Lengthen Shorten

Stresses Compressive Tensile

Temperature Increase Decrease

Hook loading Slack off Pickup

Table 2: Tubing Sign Convention

Forces. The actual force (Fa) in the tubing at the bottom of the string is dependent on the

pressures inside and outside of the tubing and the areas exposed to those pressures. This force

can be calculated with Eq.1

Fa = Pi (Ap-Ai) - Po (Ap-Ao) (1)

Where:

Fa = actually existing pressure force of a tubing string, lb

Pi = pressure inside the tubing at the packer, psi

Po = pressure outside the tubing at the packer, psi

Ai = inside tubing area, in.2

Ao = outside tubing area, in.2

Ap = packer bore area, in.2

A buckling force (Fb) is defined in Eq. 2

Fb = Ap (Pi - Po) (2)

Where:

Fb = buckling force, lb

Pi = change in pressure inside the tubing at the packer, psi Po = change in pressure outside the tubing at the packer, psi

Eq. 2 indicates that the buckling forces increase when the pressure inside the tubing string is

raised, as in the case of squeeze conditions.

Length Changes. Tubing hanging in a well that contains no fluids will stretch to some length

greater than the original length when the pipe was sitting on the racks. The pipe will be in

tension at the top but will not have stresses at the bottom. Pressure and temperature changes

resulting from normal operations induce length changes that must be evaluated since they

affect the stresses.

Packer and completion fluids apply pressures that cause a length change, L1. This change can be calculated with Hooke's law, as described in Eq. 3:

(3)

Where:

L = length of tubing to packer, in.

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

As = cross-sectional area of tubing, in.2

L1 = length change resulting from Hooke's law, in.

The cross-sectional area, As for common tubing sizes can be found in Table 3. This length

change is often termed the piston effect.

Buckling will cause a length change defined as L2. If the buckling force is less than zero:

Fb 0 (4)

Then buckling does not occur and no length changes occur, or:

L2 = 0

when the buckling force is less than the buoyed weight of the tubing string, or:

Fb Wf L (5)

Then the length change, L2, is calculated from Eq. 6:

(6)

Where:

L2 = length change due to helical buckling, in. r = tubing-to-casing radial clearance, in.

Wf = buoyed tubing weight, lb/in.

Table 3: Tubing Constants

Pressure changes inside and outside of the tubing cause length change L3. This effect is called ballooning and results from radial pressure flow. The value, L3, can be calculated from Eq.7

(7)

Where:

L3= length change due to ballooning, in.

i = change in fluid density inside the tubing, psi/in.

o = change in fluid density outside the tubing, psi/in. R = ratio of tubing OD/ID

v = Poisson's ratio for steel, v = 0.3

= tubing friction pressure, psi/in.

The tubing friction pressure, , is considered a constant and is positive when the flow is down the tubing. The worst case for ballooning length changes occur when is zero.

Temperature changes cause the tubing to elongate or contract. The amount of length change,

L4, caused by temperatures can be calculated with Eq. 8:

L4 = LT (8)

Where:

L4 = length changes due to temperature, in. T = average temperature change, F = coefficient of thermal expansion, 6.910-6/F for steel

The total length changes, L, caused by pressure and temperatures can be calculated with Eq. 9:

L=L1+L2+L3+L4 (9)

The value, L, does not account for slack-off or pickup-related changes.

Slack-off:

Field experience has shown that normal production operations may shorten the tubing. If the

seal assembly is not anchored into the packer, the tubing may shorten just enough to pull the

seal out of the packer. To avoid this, it has become a practice to lower some additional tubing

weight on the packer. This procedure is called slack-off.

Slack-off weight often ranges from 10,000-30,000 lb and will vary, depending on the

producing and tubing conditions. The slack-off force is defined as Fs. The length change,

L5, associated with slack-off weight can be calculated from Eq.10:

(10)

Where:

L5 = length change due to slack-off, in. WI = initial buoyed tubing weight, psi/in.

Fs = slack-off weight, lb

8I = inertia term

The minimum required seal assembly length can be calculated from Eq. 11:

LT=L+L5 = Ll + L2 + L3 + L4 + L5 (11)

Tuhing-to-Packer Forces. The total length changes, LT, may create an additional force defined as a tubing-to-packer force, Fp. If the length change, LT, causes the tubing to shorten, Fp is zero. However, if LT signifies a tubing elongation and the packer restrains such movement, a packer force is developed.

Further, if Fp is zero, then:

Fa*= Fa (12)

Fb*= Fb (13)

Where Fa* and Fb* are the actual and buckling forces resulting from no packer restraint.

However, in the case of packer restraint:

Fa*= Fa + Fp (14)

Fb*= Fb + Fp (15)

Fp is calculated in the same manner as the mechanically applied force necessary to move the

tubing back to its original, landed position through the distance -LT.

Effects of Buckling:

A common calculation associated with tubing is to determine the neutral point, n, or the point

above which buckling does not occur.

The neutral point can be calculated as follows:

For Fb*< Wf L:

n = Fb*/(12Wf)

For Fb* Wf L:

n = L/12

The buckled pitch, , which is the distance between spirals at the bottom of the string, is calculated as follows:

(16)

The value can be used to determine the length of logging tools that can be run through the bottom section of the tubing.

Stress Calculations:

Determination of the bending stress at the bottom of the tubing is calculated as follows:

If Fb* 0:

b = 0

If Fb* 0:

(17)

Where:

b = bending stress at the outer fiber of the tubing, psi do = tubing outer diameter, in.

I = moment of inertia, in.4

[I= /64 (do4-di

4)]

The axial stress, a is as follows:

a = Fa*/As (18)

An evaluation of a and b at the top of the tubing must account for the total string weight in the various fluids.

Buckled pipe will become permanently corkscrewed if the stress at the outer walls of the pipe

exceeds the yield strength of the pipe. Therefore, the internal and external combined stresses,

Si and So, respectively, must be determined before making a pipe selection. Si and So are

calculated as follows:

(19)

(20)

The maximum stresses are obtained from Eqs. 19 and 20 by choosing the sign () that gives

the largest value to the square root. The bending stress due to helical buckling produces both

a compressive () stress on the inside of the helix and a tensile (-) stress on the outside of the

helix. The maximum combined fiber stress will occur on either the inside or outside of the

helix, depending on whether the axial and pressure stresses are compressive or tensile.

Q.1 Consider the conditions described in Table 1. Using the following information, evaluate

the stresses involved in the tubing and select a tubing grade.

Use a stress design factor of 1.1.

Tubing size = 2.875 in.

Tubing weight = 6.4 lb/ft

Casing ID = 6.151 in.

Packer depth = 10,000 ft

Packer type = Baker Model D

Slack-off weight = 20,000 lb

Seal type = anchored seals

Packer bore = 2.375 in.

Q.2 Show that burst, collapse, and tension values are overdesigned when using stress as the

controlling criteria. Use Q.1. The maximum properties for J-55, 2.875-in., 6.4-lb/ft tubing is

as follows:

Burst = 7,260 psi Collapse = 7,680 psi

Tension = 99,6601b