Well TubingIntroduction

Most oil wells produce reservoir fluids through tubing strings. This is mainly because tubing strings provide good sealing performance and allow the use of gas expansion to lift oil. Gas wells produce gas through tubing strings to reduce liquid loading problems.

Tubing strings are designed considering tension, collapse, and burst loads under various well operating conditions to prevent loss of tubing string integrity including mechanical failure and deformation due to excessive stresses and buckling.

This chapter presents properties of the American Petroleum Institute (API) tubing and special considerations in designing tubing strings.

Strength of Tubing

The API defines ‘‘tubing size’’ using nominal diameter and weight (per foot). The nominal diameter is based on the internal diameter of tubing body. The weight of tubing determines the tubing outer diameter.

Steel grades of tubing are designated to H-40, J-55, C-75, L-80, N-80, C-90, and P-105, where the digits represent the minimum yield strength in 1,000 psi. Table 9.1 gives the tensile requirements of API tubing.

The minimum performance properties of API tubing are listed in Appendix B of this book.

The tubing collapse strength data listed in Appendix B do not reflect the effect of biaxial stress. The effect of tension of the collapse resistance is analyzed as follows.

Consider a simple uniaxial test of a metal specimen as shown in Fig. 9.1, Hooke’s Law applies to the elastic portion before yield point:

where σ, ε, and E are stress, strain, and Young’s modulus, respectively. The energy in the elastic portion of the test is

where P, A, L, V, and Δl are force, area, length, volume, and length change, respectively. However, using Hooke’s Law, we have

To assess whether a material is going to fail, we use various material failure criteria. One of the most important is the Distortion Energy Criteria. This is for 3D and is

For our case of the uniaxial test, we would have

Then from Eq. (9.4), we would get

If the failure of a material is taken to be when the material is at the yield point, then Eq. (9.6) is written

where σy is yield stress. The definition of an ‘‘equivalent stress’’ is the energy level in 3D, which is equivalent to the criteria energy level. Thus,

where σe is the equivalent stress. The collapse pressure is expressed as

where D is the tubing outer diameter (OD) and t is wall thickness. For the 3D case, we can consider

where σe is the equivalent stress for the 3D case of

Consider the case in which we have only tensile axial loads, and compressive pressure on the outside of the tubing, then Eq. (9.12) reduces to

Further, we can define

Tubing Design

Tubing design should consider tubing failure due to tension, collapse, and burst loads under various well operating conditions. Forces affecting tubing strings include the following:

1. Axial tension due to weight of tubing and compression due to buoyancy

2. External pressure (completion fluids, oil, gas, formation water)

3. Internal pressure (oil, gas, formation water)4. Bending forces in deviated portion of well5. Forces due to lateral rock pressure6. Other forces due to thermal gradient or dynamics

Tension, Collapse, and Burst Design

The last three columns of the tables in Appendix B present tubing collapse resistance, internal yield pressure, and joint yield strength.

These are the limiting strengths for a given tubing joint without considering the biaxial effect shown in Fig. 9.2.

At any point should the net external pressure, net internal pressure, and buoyant tensile load not be allowed to exceed tubing’s axial load-corrected collapse resistance, internal yield pressure, and joint yield strength, respectively.

Tubing strings should be designed to have strengths higher than the maximum expected loads with safety factors greater than unity.

In addition, bending stress should be considered in tension design for deviated and horizontal wells.

The tensile stress due to bending is expressed as

Because of the great variations in well operating conditions, it is difficult to adopt a universal tubing design criterion for all well situations.

Probably the best design practice is to consider the worst loading cases for collapse, burst, and tension loads that are possible for the well to experience during the life of the well.

It is vitally important to check the remaining strengths of tubing in a subject well before any unexpected well treatment is carried out.

Some special considerations in well operations that affect tubing string integrity are addressed in the sections that follow.

Buckling Prevention during Production

A completion fluid is in place in the annular space between the tubing and the casing before a well is put into production.

The temperature at depth is T = Tsf + GTD, where GT is geothermal gradient. When the oil is produced, the temperature in the tubing will rise.

This will expand (thermal) the tubing length, and if there is not sufficient landing tension, the tubing will buckle.

The temperature distribution in the tubing can be predicted on the basis of the work of Ramey (1962), Hasan and Kabir (2002), and Guo et al. (2005). The latter is described in Chapter 11.

A conservative approach to temperature calculations is to assume the maximum possible temperature in the tubing string with no heat loss to formation through annulus.

Example Problem 9.2 Consider a 27⁄8 in. API, 6.40 lb/ft Grade P-105 non-upset tubing anchored with a packer set at 10,000 ft.

The crude oil production through the tubing from the bottom of the hole is 1,000 stb/day (no gas or water production).

A completion fluid is in place in the annular space between the tubing and the casing (9.8 lb/ gal KCl water).

Assuming surface temperature is 60 0F and geothermal gradient of 0.01 0F/ft, determine the landing tension to avoid buckling.

Solution The temperature of the fluid at the bottom of the hole is estimated to be

The average temperature of the tubing before oil production is

The maximum possible average temperature of the tubing after oil production has started is

This means that the approximate thermal expansion of the tubing in length will be

where β is the coefficient of thermal expansion (for steel, this is βs = 0:0000065 per 0F). Thus,

To counter the above thermal expansion, a landing tension must be placed on the tubing string that is equivalent to the above.

Assuming the tubing is a simple uniaxial element, then

Thus, an additional tension of 17,667 lbf at the surfacemust be placed on the tubing string to counter the thermal expansion.

It can be shown that turbulent flow will transfer heat efficiently to the steel wall and then to the completion fluid and then to the casing and out to the formation.

While laminar flow will not transfer heat very efficiently to the steel then out to the formation. Thus, the laminar flow situations are the most likely to have higher temperature oil at the exit.

Therefore, it is most likely the tubing will be hotter via simple conduction. This effect has been considered in the work of Hasan and Kabir (2002).

Obviously, in the case of laminar flow, landing tension beyond the buoyancy weight of the tubing may not be required, but in the case of turbulent flow, the landing tension beyond the buoyancy weight of the tubing is usually required to prevent buckling of tubing string. In general, it is good practice to calculate the buoyant force of the tubing and add approximately 4,000-5,000 lbf of additional tension when landing.

Considerations for Well Treatment and Stimulation

Tubing strings are designed to withstand the harsh conditions during wellbore treatment and stimulation operations such as hole cleaning, cement squeezing, gravel packing, fracpacking, acidizing, and hydraulic fracturing.

Precautionary measures to take depend on tubing–packer relation. If the tubing string is set through a non-restraining packer, the tubing is free to move.

Then string buckling and tubing–packer integrity will be major concerns. If the tubing string is set on a restraining packer, the string is not free to move and it will apply force to the packer.

The factors to be considered in tubing design include the following:

Tubing size, weight, and grade

Well conditions

o Pressure effect

o Temperature effect

Completion method

o Cased hole

o Open hole

o Multitubing

o Packer type (restraining, non-restraining)

Temperature Effect

As discussed in Example Problem 9.2, if the tubing string is free to move, its thermal expansion is expressed as

If the tubing string is not free to move, its thermal expansion will generate force. Since Hook’s Law gives

substitution of Eq. (9.22) into Eq. (9.21) yields

for steel tubing.

Pressure Effect

Pressures affect tubing string in different ways including piston effect, ballooning effect, and buckling effect.

Consider the tubing–pack relation shown in Fig. 9.3. The total upward force acting on the tubing string from internal and external pressures is expressed as

The total downward force acting on the tubing string is expressed as

where Ai is the inner area of tubing. The net upward force is then

During a well treatment operation, the change (increase) in the net upward force is expressed as

If the tubing string is anchored to a restraining packer, this force will be transmitted to the packer, which may cause packer failure.

If the tubing string is free to move, this force will cause the tubing string to shorten by

which represents tubing string shrinkage due to piston effect.

As shown in Fig. 9.4a, the ballooning effect is due to the internal pressure being higher than the external pressure during a well treatment.

The change in tensile force can be expressed as

If the tubing string is set through a restraining packer, this force will be transmitted to the packer, which may cause packer failure.

If the tubing string is free to move, this force will cause the tubing string to shorten by

As illustrated in Fig. 9.4b, the buckling effect is caused by the internal pressure being higher than the external pressure during a well treatment.

The tubing string buckles when FBK = Ap(pi - po) > 0.

If the tubing end is set through a restraining packer, this force will be transmitted to the packer, which may cause packer failure.

If the tubing string is not restrained at bottom, this force will cause the tubing string to shorten by

which holds true only if FBK is greater than 0, and

Total Effect of Temperature and Pressure

The combination of Eqs. (9.22), (9.28), (9.30), and (9.31) gives

which represents the tubing shortening with a nonrestrainingpacker.

If a restraining packer is used, the total tubing force acting on the packer is expressed as