Changing the mode of a well (producer, injector, shut-in, or treating) causes changes in temperature and pressure inside and outside the tubing. This can create length and force changes in the tubing string that can potentially affect the packer and downhole tools.
Impact of tubing length and force changes
After the packer is installed and the tubing landed, any operational mode change will cause a change in length or force in the tubing string. The resultant impact on the packer and tubing string is dependent on:
- How the tubing is connected to the packer
- The type of packer
- How the packer is set
- Tubing compression or tension left on the packer.
The length and force changes can be considerable and can cause tremendous stresses on the tubing string, as well as on the packer under certain conditions. The net result could reduce the effectiveness of the downhole tools and/or damage the tubing, casing, or even the formations open to the well. Failure to consider length and force changes may result in costly failures of such operations as:
Length and force changes
Potential tubing-length changes must be understood to determine the length of seal necessary to remain packed off in a polished sealbore packer, or to prevent tubing and packer damage when seals are anchored in the packer bore. Potential induced forces need to be calculated to prevent:
There are four factors that tend to cause a change in the length or force in the tubing string
Buckling will shorten the tubing string; however, the other effects may tend to lengthen or shorten the string depending on the application of the factors. As long as the tubing is allowed to move in the packer bore, the temperature and ballooning effects will only have an impact on tubing-length changes, but, if movement is prevented (or restrained) at the packer, these two factors would then create a force.
It is important to remember that a string of tubing landed in any packer is initially in a neutral condition, except for any subsequent mechanical strain or compression loads applied by the rig operator. After the tubing is landed, the factors that cause changes in length or force are always the result of a change in temperature and pressure.
Piston Effect
The length change or force induced by the piston effect is caused by pressure changes inside the annulus and tubing at the packer, acting on different areas (Fig. 1). The length and force changes can be calculated as follows:
....................(1)and 
....................(2)
....................(2)where ΔL1 = length change because of the piston effect, F1 = force change because of the piston effect, L = tubing length, E = modulus of elasticity (30,000,000 for steel), As = cross-sectional area of the tubing wall, Ap = area of the packer bore (values for common sizes can be found in Table 1), Ai = area of the tubing ID, Ao = area of the tubing OD, Δpi = change in tubing pressure at the packer, and Δpo = change in annulus pressure at the packer.
Note that the length change ΔL1 is a product of L/EA s and the piston force (F1). The piston force is the sum of two pressures acting on two areas—one for the tubing and one for the annulus. The area acted upon by changes in pressure in the tubing is the cross-sectional area between the area of the packer bore and the area of the tubing ID in square inches (Ap –Ai). The area acted upon by changes in pressure in the annulus is the cross-sectional area between the area of the packer bore and the area of the tubing OD in square inches (Ap –Ao).
Fig. 1(a) shows a large-bore packer with a tubing string that has both a smaller OD and ID than the packer bore. In this instance, annulus pressure causes downward force, while tubing pressure causes an upward force. For a small-bore packer, this situation is reversed (Fig. 1(b)). The force greatest in magnitude will determine the resulting direction of action. An accurate schematic of the tubing and packer bore for each case should be made for proper determination of areas, forces, and the resulting direction of action.
It is possible to eliminate the forces generated on the tubing string by the piston effect by anchoring the seals in the packer bore. In a string that is restrained at the packer from movement in either direction, the piston effect on the tubing string is zero. All the forces are now being absorbed or contained completely within the packer.
Buckling Effects
Tubing strings tend to buckle only when the internal tubing pressure (pi) is greater than the annulus pressure (po). The result is always a shortening of the tubing string, but the actual force exerted is negligible. The decrease in length occurs because of the tubing string being in a spiral shape rather than straight. The tubing-length change is calculated with the following:
....................(3)where ΔL2 = length change because of the buckling effect; r = radial clearance between tubing OD and casing ID, [ (IDC – ODt)/2]
- Ap = area of the packer bore; Ai = area of the tubing ID; Ao = area of the tubing OD; Δpi = change in tubing pressure at the packer; Δpo = change in annulus pressure at the packer; E = modulus of elasticity (30,000,000 for steel); I = moment of inertia of tubing about its diameter[
I = π/64 (D4 – d4, where D is the tubing OD and d is the tubing ID*]
- Ws = weight of tubing per inch*; Wi = weight of fluid in tubing per inch*; and Wo = weight of displaced fluid per inch.* (* = values for common tubing sizes can be found in Tables 2 and 3).
Ballooning and Reverse Ballooning
The ballooning effect is caused by the change in average pressure inside or outside the tubing string. Internal pressure swells or "balloons" the tubing and causes it to shorten. Likewise, pressure in the annulus squeezes the tubing, causing it to elongate. This effect is called "reverse ballooning." The ballooning and reverse ballooning length change and force are given by
....................(4)and 
....................(5)
....................(5)where ΔL3 = length change because of ballooning/reverse ballooning, F3 = force change because of ballooning/reverse ballooning,L = tubing length, γ = Poisson ’ s ratio (0.3 for steel), E = modulus of elasticity (30,000,000 for steel), Δpia = change in average tubing pressure, Δpoa = change in average annulus pressure, Ai= area of the tubing ID, Ao = area of the tubing OD, and R = ratio of tubing OD to ID (given in Table 2) for common tubing sizes and weights. The ballooning effect will always result in tubing-length changes, but it does not become a force unless the tubing movement is restrained at the packer.
Temperature Effect
Thermal expansion or contraction causes the major length change in the tubing. Heated metal expands, and cooled metal contracts. In a long string of tubing with a temperature change over its entire length, this contraction or elongation can be considerable. The three operational modes that influence temperature effect are producing, injecting (water, gas, or steam), and treating.
The change in tubing length because of temperature effect is calculated as follows:
....................(6)where ΔL4 = change in tubing length, L = tubing length, β = coefficient of thermal expansion (0.0000069 for steel), and Δt = change in average temperature.
Length changes are calculated readily if the average temperature of the tubing can be determined for the initial condition and then again for future operations. The average string temperature in any given operating mode is approximately one-half the sum of the temperatures at the top and the bottom of the tubing. Thus, in the initial condition, the average temperature would be based upon the mean yearly temperature and the BHT. The mean yearly temperature is generally considered to be the temperature 30 ft below ground level; Δt is the difference between the average temperatures of any two subsequent operating modes.
If tubing movement is constrained, forces will be introduced as a result of the temperature change. The temperature-induced force is
....................(7)where F4 = pounds force (tensile or compression, depending on the direction of Δt ), AS = cross-sectional area of the tubing wall, and Δt = change in average tubing temperature.
Net results of combined effects
The net or overall length change (or force) is the sum of the length changes (or forces) caused by the temperature, piston, and ballooning effects. The direction of the length change for each effect (or action of the force) must be considered when summing them. It follows that for a change in conditions, the motion (or force) created by one effect can be offset, or enhanced, by the motion (or force) developed by some other effect.
Mosely presented a method for graphically determining the length and force changes as a result of buckling and ballooning (L2 ,L3, and F3). This method is particularly useful on a fieldwide basis, where wells have the same-size tubing, casing, and packers.
When planning the sequential steps of a completion or workover, care should be taken to consider the temperatures and pressures in each step once the tubing and packer systems become involved. By careful selection of the packer bore and use of annulus pressures, one pressure effect (or a combination of pressure effects) could be used to offset the adverse length or force change of another effect.
References
- Packer Calculations Handbook. 1992. Baker Oil Tools Div.
- Lubinski, A., Althouse, W.S., and Logan, J.L. 1962. Helical Buckling of Tubing Sealed in Packers. J. Pet Tech 14 (6): 655-670. SPE-178-PA. http://dx.doi.org/10.2118/178-PA.
- Moseley, N.F. 1973. Graphic Solutions to Tubing Movement in Deep Wells. Petroleum Engineering Intl: 59.
General references
Allen, T. and Roberts, A.P. 1993. Production Operations, fourth edition, I and II.
Factors and Conditions Which Cause Seal Assemblies Used in Downhole Enviornments to Get Stuck. Baker Oil Tools—Engineering Tech Data Paper No. CS007.
Patton, L.D. and Abbott, W.A. 1985. Well Completions and Workovers: The Systems Approach, second edition, 57–67. Dallas: Energy Publications.
