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: 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
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.
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
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 δ = tubing friction pressure, psi/in.
The tubing friction pressure, δ, is considered a constant and is positive when the flow is down the tubing. The worst case for ballooning length changes occur when δ 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 = L∆Tβ (8)
Where:
∆L4 = length changes due to temperature, in. ∆T = average temperature change, °F
β = coefficient of thermal expansion, 6.9×10-6
/°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
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, λ, which is the distance between spirals at the bottom of the string, is calculated as follows:
(16) The value λ 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:
σb = 0 If Fb*› 0:
(17) Where:
σb = bending stress at the outer fiber of the tubing, psi do = tubing outer diameter, in.
I = moment of inertia, in.4
[I= π/64 (do4-di4)]
The axial stress, σa is as follows:
σa = Fa*/As (18)
An evaluation of σa and σb 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
