Study examines causes of upheaval buckling in shallow subsea PIP lines

Feb. 11, 2008
Temperature, initial slope imperfections, and downward restraints on a pipeline all affect its propensity for upheaval buckling.

Temperature, initial slope imperfections, and downward restraints on a pipeline all affect its propensity for upheaval buckling. A restrained pipeline is subject to compressive loads as the temperature of the transported medium rises.

A pipeline laid on the seabed is likely to experience lateral buckling. Partially or fully burying the pipeline restrains it laterally in the horizontal plane, but upheaval buckling is likely where initial imperfections of the seabed exist.

Hobbs derived analytical solutions for the buckling and post-buckling behavior of a heated pipeline assuming a buckling curve for the pipeline.1 Hobbs established the relationship between the buckling temperature and length of buckle considering the axial pipe-soil interaction. Taylor-Gan studied the effects of initial imperfection and defined the limitation for Hobbs’ relationship.2 Palmer et al. developed a semi-empirical relationship for the downward restraints required to prevent upheaval buckling as a function of the initial imperfection and operating temperature.3 These studies addressed single pipe.

Design temperatures of offshore pipelines approaching 150° C. or more have prompted use of pipe-in-pipe systems to prevent formation of hydrate and wax deposits in development of hot oil fields in both shallow and deep water. Thermal insulation such as polyurethane foam fills the annulus between the inner and outer pipes.

This article focuses on upheaval buckling of a pipe-in-pipe system in shallow water and develops and verifies relationships among critical temperature, initial imperfection, and downward restraints of the pipeline. The article also discusses countermeasures for preventing upheaval buckling of offshore pipelines in shallow water and develops an analytical solution for determining the spacing of intermediate spools in a PIP system.

Single pipe

Height as a function of distance can describe the shape of a pipeline. Considering a pipeline as a beam, Equation 1 expresses the relationship between the axial compressive force and laterally distributed load.

Compressive load along with initial imperfections cause upheaval buckling of a pipeline. Equation 2 expresses the initial deformation assumed for a hill-type imperfection.

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Palmer et al. derived the downward restraints to prevent upheaval buckling by substituting Equation 2 into Equation 1.3

An idealized curve for the initial deformation of the pipe provides the basis for developing Equation 3. In practice, initial deformation of an offshore pipeline differs somewhat from the known deformation of the seabed. Finite element models developed for a pipeline buried along an idealized hill on the seabed attempted to use the shape of the seabed as the initial imperfection of the pipeline, evaluating the differences in the shapes of the pipeline and seabed as well as their effects on buckling potential.

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The pipeline used is 4-km long with both ends fixed in the axial direction. It has a 406.4-mm OD, 7.1-mm WT, and submerged weight of 1,778.1 Newtons/m. The Young’s modulus of the pipe is 2.06 × 1011 pascals and the friction coefficient between the pipe and surrounding soil is 0.5. Equation 2 defines the initial imperfection of the seabed, shown in Fig. 1 with a length of 70 m and heights of 0.2 m, 0.5 m and 0.8 m, respectively.

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Fig. 2 shows the critical temperature vs. the imperfection height of the seabed. For a small height, the numerical solution lies very close to the analytical solution. As the hill height increases, the difference between the two solutions increases. The increasing embedment of the pipe around the top as the height of imperfection increases and the difference of peak height between the pipeline and seabed cause this. Using the seabed curve as the initial imperfection of the pipeline leads to a conservative critical temperature. Such an approach, however, is still feasible in engineering as the difference is less than 10° C.

Pipe-in-pipe

In a pipe-in-pipe system, thermal insulation materials fill the annulus between the inner pipe and outer pipe. The outer pipe normally maintains ambient temperature, while the inner pipe assumes the same temperature as the medium. Temperature changes in the medium cause axial deformations of the PIP system around the pipe ends or around the bend where a pipeline changes direction.

In addition to relative deformation between the outer pipe and the seabed, relative deformation also occurs between the inner and outer pipes, the compressive load of the inner pipe being partially transferred to the outer pipe in tension. Axial compressive forces decrease towards the pipe end or bend as axial deformations develop.

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Locations away from the end or bend where there are no relative displacements among the seabed, inner, and outer pipes show the system’s highest systemic axial compressive loads for a given temperature rise. These locations are more susceptible to upheaval buckling on an uneven seabed. The outer pipe does not take any axial thermal loads and only leads to increases in bending stiffness.

Equations 4 and 5 express the forces affecting a pipe-in-pipe system.

Numerically modeling the two sets of pipe-in-pipe systems listed in Table 1, including weights per unit length, tests these equations. The weight of the inner pipe includes the weight of medium (oil) and the weight of the outer pipe is the submerged weight (subtracting buoyancy).

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Both models use a 4,000-m pipeline with both ends fixed in the axial direction. The friction coefficient between the inner pipe and outer pipe is 0.2, and the friction coefficient between the outer pipe and seabed is 0.5.

Fig. 3 shows the critical temperature used in the first model for the three heights in Fig. 1, preserving the temperature difference of 10° C. or less referred to in the analytical results of Equations 4 and 5.

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The second model considers a 100-m imperfection caused by the high bending stiffness of the pipes, using the same imperfection heights used in the first model. Fig. 4 shows the critical temperatures from both numerical and analytical approaches. As shown in Figs. 3 and 4, the critical temperature increased due to the high bending stiffness of the PIP system in comparison with the single pipe, and the analytical solutions match reasonably well with the numerical solutions.

Limitations

Equation 4 requires an initial deformation of the pipeline in a PIP system comparable to the initial imperfection of the seabed. A short imperfection combined with bending stiffness, however, causes suspension of the pipeline around its toes to deviate from the shape of the seabed.

A given lifting height off a flat seabed requires the pipeline be suspended under its submerged weight. Equation 6 estimates the suspended pipe length corresponding to height, δ.

Numerical models developed for an imperfection height of 0.8 m verified the minimum length of the initial imperfection applicable for Equation 4. Both the numerical model and analytical help calculate the critical temperature under the submerged weight of pipes. Figs. 5a and b show the results for the first and second models, respectively.

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The minimum length from Equation 6 can act as a cut-off point for Equation 4, below which the shape of pipe is dominated by its bending stiffness and the critical temperatures are more or less the same. Equation 7 calculates the critical compressive load leading to upheaval buckling under a given initial imperfection in these circumstances.

Equations 6 and 7 apply to partially or fully buried offshore pipelines. They also apply to a single pipe in which only the bending stiffness of the pipe is considered. Pipelines laid on seabed, however, are likely to experience lateral buckling, making these equations not applicable.

Intermediate spools

Expansion loops (i.e., intermediate spools) may reduce the axial thermal stresses in the inner pipe of a PIP system with high design temperatures. Expansion loops place the outer casing pipe segments between the loops under tension during operation. These tension forces tend to increase the critical temperature and reduce the buckling potential of the PIP system. Equation 8 provides the maximum compressive load of a PIP system with intermediate spools.

A bulkhead typically installed in the straight segment near the spool connects the inner and outer pipes. Equation 9 provides the bulkhead’s equilibrium.

Soil restraints in the axial direction also control the outer pipe’s end displacement at the spool (Equation 10).

The effective length, LE, in Equation 10 represents no more than the half spacing of intermediate spools (Equation 11).

A PIP system designed for high temperatures functions best when the outer pipe is put in tension (i.e., P2 > 0) by choosing a relatively short interval for intermediate spools (Le = 0.5Ls).

Pipeline engineering casts the axial resistance from the expansion loop, Rspool, as negligible, simplifying Equation 8 as Equation 12.

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Equation 12 calculates the maximum compressive force, Pmax, for a selected spacing, Ls, in the PIP system. A maximum force larger than the critical load, Pcr, from Equation 7, requires reduction of the spacing between the spools. Fig. 6 shows the maximum compressive force in the PIP system from the simplified and numerical approaches. Neglecting the resistance from the spool makes the maximum compressive force from the simplified approach slightly less than from the numerical.

Equations 8-12 also apply to a PIP system with a dogleg; spacing Ls acting as the distance between the dogleg and adjacent expansion loop or another dogleg in a short PIP system without an intermediate spool.

Design example

Engineering offshore pipelines without intermediate spools uses a given temperature of the medium and a seabed profile derived from a site survey. Equation 5 can calculate the maximum compressive force, while Equation 6 calculates the minimum length for the pipeline in conformance with the hill-type seabed. Equation 7 calculates the downward restraints required for the system to avoid upheaval buckling.

Partially exposed pipelines on the seabed use the submerged weight of the pipe and medium as the downward restraint. Buried pipelines use the submerged weight of the pipe and medium as well as the soil over the pipe.

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Model 1 in Table 1 represents pipelines crossing a 70-m imperfection on the seabed with 0.5 m and 1.0 m soil covers, respectively. Equation 7 calculates the critical temperatures, shown in Fig. 7 for three heights of imperfection along with results from the finite-element approach. The results show the PIP system can transport oil at a temperature up to 120° C., a typical burial depth of 1.0 m, and a corresponding slope of imperfection is 0.011 (0.38-m high and 35-m long).

If the slope of the imperfection is more than 0.011, burying the pipeline deep into the seabed around the hill top (overbend of the pipeline) provides the most effective means of preventing bucking. Doing so not only reduces the height of the initial imperfection, but also increases the downward restraints.

Concrete mats, sand bags, or cobbles placed on top of the pipeline at the hilltop can also act as restraining means. A very hard seabed where hydraulic jetting is not possible might use pre-plough or trenching equipments to reduce the imperfection.

Equation 7 verifies the effectiveness of the chosen means.

References

  1. Hobbs, R.E., “In-Service Buckling of Heated Pipelines,” ASCE Journal of Transportation Engineering, Vol. 110, pp. 175-189, 1984.
  2. Taylor, N., and Gan, A., “Submarine Pipeline Buckling Imperfection Studies,” Thin-Walled Structures, Vol.4, pp. 295-323, 1986.
  3. Palmer, A.C., Ellinas, C.P., Richards, D.M., and Guijt, J., “Design of Submarine Pipelines Against Upheaval Buckling,” OTC 6335, Offshore Technology Conference, Houston, May 7-10, 1990.
  4. Raoof, M., and Maschner, E., “Thermal Buckling of Subsea Pipelines,” OMAE-ASME Pipeline Technology, Vol. 5, 1993.
  5. Sriskandarajah, T., Anurudran, G., Ragupathy, P., and Wilkins, R., “Design Considerations in the Use of Pipe-In-Pipe Systems for HP/HT Subsea Pipelines,” International Society of Offshore and Polar Engineers conference, Brest, France, May 30-June 4, 1999

The authors

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Jack X. Liu ([email protected]) is a visiting professor at China University of Petroleum, Beijing, and president of Liu Advanced Engineering LLC, Houston. He has also served as a principal engineer at Technip USA. He holds a PhD (1996) from Rensselaer Polytechnic Institute, Troy, NY, and a BS (1987) from Huazhong University of Science and Technology, China. He is a registered professional engineer in Texas.

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H.M. Zhang ([email protected]) is a chief engineer in the sales department at Shengli oil field. He has also severed as a manager of the transporting oil company of Shengli. He holds a BS from HuaDong Petroleum Institute (1985) and an MS from China University of Petroleum (2003).

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Q.R. Meng ([email protected]) is an engineer at Rong-Sheng Machinery Manufacture Ltd. of Huabei oil field, RenQiu. She holds an MS (2006) from China University of Petroleum (Beijing).

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Hong Zhang ([email protected]) is a professor at China University of Petroleum, Beijing. He holds a PhD (2003) from China University of Petroleum, Beijing. He is a member of the American Society of Mechanical Engineers.