Using vertical upset method to design for lateral buckling in HP/HT pipelines

Based onDNV-OS-F101 code and using available information, SLT-Engineering developed a simplified way to address the design of safe HP/HT pipelines.

Below are design parameters set for lateral buckling of the pipeline:

1. The buckling force (maximum pipeline axial force capacity) should be equal to a minimum of the Hobbs mode infinity and out-of-straightness model.

2. Design feed-in length of each buckle should equal the maximum feed-in-length into the buckle which does not cause pipeline failure under all limiting states.

3. The probability of maximum feed-in length exceeding the design feed-in-length shall be less than 10-4.

Lateral buckling analysis

Soil resistance against pipeline movement is divided into two main sections – breakout and residual. The lateral resistance model of soil is based on the model and recommendations of the SAFEBUCK joint industry project. Initial pipeline embedment is calculated using

Where, z is the initial penetration of pipe, D the pipe outside diameter, St the soil sensitivity, V the vertical load on the pipeline inclusive of dynamic load during pipeline installation, and Su the undrained shear strength at the bottom of the pipe.

The lateral breakout and residual resistances of soil then may be calculated using

Where,γ is the submerged soil unit weight, v the vertical load on pipe, and Su_1D the undrained shear strength of soil at one pipe diameter below seabed.

Mobilization of breakout resistance is assumed within a pipe movement of less than half of a diameter, while residual resistance occurs within three to five diameters.

For axial resistance of the pipeline the soil model by Brennodden20 is used. According to this model, maximum and residual axial resistance of soil may be calculated using

The mobilization of axial breakout resistance is within a pipe movement of less than 0.05 of a pipe diameter, while residual resistance occurs at 1.2 times the diameter of pipe. Uncertainty of the soil model is treated based on recommendations by the SAFEBUCK JIP¹⁰.

Lower bound axial capacity of the pipeline to withstand lateral buckling is calculated using

S = min (S_H∞, S_OOS)

Where,

Where, E is the elastic modulus of the pipeline material, W the submerged weight per unit length of the pipeline, μ the lateral friction coefficient, I the pipeline moment of inertia, As the pipeline cross section area, FD the drag force per unit length on the pipeline, FL the lift force per unit length on the pipeline, and ∫LLB the lower bound lateral soil resistance.

The pipeline may buckle if the maximum axial effective force is higher than the axial capacity of the pipeline.

To calculate maximum allowable strain, the following key failure modes (except pressure containment and external pressure collapse that were fulfilled during the early stage of pipeline design) are considered:

Local buckling

As most applied loadings on the pipeline are displacement-controlled, a strain based design criteria using DNV-OS-F101 for local buckling analysis considers these assumptions:

1. Hoop component of stress and resultant strain are kept within the allowable limit obtained from load controlled criteria.

2. Environmental loads are applied to the buckle free span in the zones around the buckle triggers. Effects of these loads on the resultant strain should be insignificant.

Fatigue

HP/HT pipelines generally are subject to two main load cycles:

1. Low cycle/high amplitude loading, mainly due to pipeline installation and startup/shutdown of the line.

2. High cycle/low amplitude loading, mainly due to environmental load and vortex induced vibration (VIV).

For low cycle fatigue analysis of the pipeline, the American Bureau of Shipping method may be used. According to ABS, the equation below may be used to assess the fatigue life of the welded structures when the plastic strain range is significant.

Where, Δε is the strain range in pipeline.

Investigations13 show that a safety factor of at least 7.0 is included in the equation.

The high cycle fatigue analysis of the pipeline spans aside the buckle triggers and is performed in accordance withDNV-OS-F101 and DNV-RP-C203 under the assumption that the weld line is in the region with the highest stress conditions.

Fracture

Engineering critical assessment is based on BS 7910 16 usingDNV-OS-F101. Based on accuracy of available examination methods, an undetectable circumferential crack with 25 mm (1 in.) length and 2.5 mm (1/10 in.) depth may be considered for fracture analysis.

Design feed-in length of each pipeline section is calculated using a virtual anchor model by finite element method considering the above mentioned limits.

Even in pipelines susceptible to lateral buckling, limit state parameters of the buckled section may be acceptable. To assess acceptability of a non-mitigated pipeline, a single buckle between two virtual anchor points on the pipeline is considered, where the feed-in into the buckle is the maximum. The buckle may be triggered by initial lateral or vertical imperfection, or by trawling load.

Calculate distance between buckle triggers using:

• Maximum allowable expansion of end sections of pipeline based on expansion spool design capacity and lower bound axial soil resistance. The first buckle trigger from each side of the pipeline is positioned to allow maximum expansion at each end of the pipeline
• Buckle triggers are positioned to limit maximum feed-in into the buckles below the design feed-in length
• If the probability of buckle formation failure at a specific buckle trigger is more than 10-4, the consequences of formation of a buckle at vicinity of the buckle trigger should be evaluated.

Buckle formation probability

In lateral buckling analysis of HP/HT pipelines, the key uncertainty is buckle formation at the expected sites. To calculate the buckle formation probability, a simplified version of the reliability model presented in Carr, et al5 is used. According to this model, the probability of buckling is:

Where, Z is the limit state function describing the buckle formation, which is obtained by recasting the buckling formation criteria. The following equation denotes the buckling limit state function.

Where, Rlat is lateral resistance against pipeline buckling, μa axial friction factor of soil, W pipeline weight per unit length, x sleeper distance to the end of line or previous sleeper, and E is axial force of the pipeline due to spool resistance or residual axial force in the previous buckle.

After positioning the buckle triggers along the pipeline route, the mitigated pipeline is analyzed to check whether the mitigation scheme works under pipeline heat-up and cool-down transients. Under certain circumstances, walking of the pipeline section between two adjacent buckle triggers (towards the cold end of the pipeline) may increase feed-in into the initiated buckle. This phenomenon cannot be captured by a virtual anchor spacing model; the whole pipeline has to be modeled for finite element analysis.

Case study

The pipeline was constructed using 12-in. API 5L-X65 line pipe. High-density concrete coating was used for pipeline stability, and its effects on pipeline strength were ignored. Design pressure and temperature distribution along the pipeline were used in the analysis. Design pressure and maximum design temperature were 201.4 barg (2,907 psi) and 120° C (248° F), respectively. Temperature profile along the pipeline was calculated based on 50% embedment. The design life of the pipelines is six years. The total number of startups and shutdowns during the lifetime of the pipeline is 24 cycles. For global buckling analysis and ratcheting analysis, isotropic strain nonlinear hardening and simplified linear kinematics strain hardening behavior of X65 were used, respectively.

Due to insufficient soil data, the following was used to estimate upper bound, median, and lower bound soil properties:

1. Investigations of available soil data in existing routes near the proposed route. These investigations indicated that the undrained shear strength of the soil along the route changed linearly with respect to the pipeline penetration, for penetration depths of less than 1 m (3.25 ft).

2. Three linear functions were fitted to the available soil data along the pipeline and defined as upper bound, median, and lower bound undrained shear strength profile of the soil.

3. Soil axial and lateral resistances were calculated based on the estimated soil properties.

Three types of Abaqus finite element models were used as follows:

1. Full finite element model of the pipeline on uneven seabed. This was used in the first and last stages of lateral buckling analysis. In the first stage, it was used to evaluate if the strain in an unwanted buckle triggered by the seabed imperfection, lateral imperfection, or trawling was within allowable worst-case loading and pipe-soil interaction conditions. In the last stage, it was used to check strain increase in the initiated buckles from hydrodynamic loads and pipeline walking. The full finite element model of the pipeline was constructed using full route geometry and seabed profile.

2. Virtual anchor spacing model. Two virtual anchor spacing models were used, the first on flat seabed and the second on flat seabed with the effects of sleepers. The first model was used to calculate:

• Feed-in into a buckle rested on seabed for different pipe-soil interaction conditions
• Relationship between the feed-in and strain level in pipeline rested on seabed for different pipe-soil interaction conditions.
  The second model was used to:
  • Check the span length on each side of the sleeper
  • Calculate maximum axial load capacity of the pipeline rested on the sleeper
  • Calculate the natural frequency of the pipeline span due to the sleeper for VIV analysis.
  3. Three dimensional solid model. This was used for ratcheting analysis and to obtain actual stress distribution in the pipeline for fracture analysis.

An Abaqus UFRIC FORTRAN subroutine was developed to model the cohesive and break-out behaviors of pipe/soil interaction model.

For full finite element model of the pipeline on uneven seabed and virtual anchor spacing models, the pipeline was split into two sections “around imperfection” and “away from imperfection”, with different element sizes to achieve reasonable accuracy.

For out-of-straightness (OOS) model lay imperfections, bend radius of 2,500 m (8,202 ft) along the Zone I, and 2,000 m (6,562 ft) along the Zone II route were assumed. These magnitudes of imperfections were set as limiting criteria for pipelay.

Calculation of allowable buckle apex strain

Allowable strain of the pipeline was calculated usingDNV-OS-F101. To calculate strain limit, axial force and internal pressure of the pipeline were set to maximum value obtained from finite element analysis, and 201.4 barg (design pressure of the pipeline), respectively.

The minimum allowable total strain in the pipeline was 2.8% from local buckling point of view.

Maximum allowable strain range for the pipeline was 1.5%.

In the absence of a mitigation technique, a single buckle between pipeline virtual anchor points was considered with the following assumptions:

• An isolated buckle is formed in the early stage of buckling
• All possible feed-in resulting from soil with upper bound axial friction is fed into the buckle considering upper bound lateral friction
• Buckle can be triggered by both vertical and horizontal imperfections. Buckle initiation by trawling was not considered since the probability around the pipeline route is very low.

Using these assumptions, total strain in the buckle was 2.85% which was unacceptable from a low cycle fatigue point of view. So, it was decided to mitigate the pipeline using a buckle initiation strategy.

Mitigation method

To overcome soil data uncertainty, it was decided to use sleepers to impose vertical out of straightness to the pipeline. Calculations showed that applying a vertical out of straightness might be insufficient in special circumstances. So, it was decided to add an in-plane imperfection to control lateral resistance on the pipeline and the direction of buckling.

The relationship between feed-in into a buckle and pipeline axial strain was calculated using finite element. Results show the introduced plastic strain in a buckle versus thermal feed-in, and that maximum strain in a buckle corresponds to the maximum lateral seabed friction coefficient. The maximum allowable feed-in into a buckle in different lateral friction coefficients was based on 1.5% total strain range obtained from low cycle fatigue analysis. Material changes due to temperature were minor.

The distance between two adjacent sleepers was calculated using an iterative process with the following criteria:

1. The distance of the first and last sleeper to the end points of the pipeline (PC04 and 11) should maintain maximum end expansion of the pipeline. These expansions were obtained from a pipeline riser design report, and were 0.8 m, and 1.2 m for the PC04 and B11 side of the pipeline, respectively. Besides, maximum feed-in into the first and last buckles triggered by the sleepers should be less than design feed-in length. Considering these criteria, the maximum distance of the first sleeper to the end point of the pipeline (PC04 side) is 1.4 m (4.5 ft).

2. Other buckle triggers were positioned for maximum feed-in in each buckle less than design feed-in length. To assist controlled buckle formation, the pipeline concrete coating around the buckle triggers was removed.

Considering the pipeline routing criteria, final positions of the sleepers were calculated.

Important parameters that affect lateral resistance of buckle triggers on the pipeline (axial force capacity of a pipeline) were:

• Sleeper height (imperfection in vertical plane)
• Friction coefficient between pipeline and sleeper
• Friction coefficient between pipeline and seabed
• Pipeline span length aside buckle triggers
• Initial imperfection in horizontal plane
• Submerged weight per unit length of pipeline.

A parametric study evaluated the effects of these on the axial force capacity of the pipeline and results went into the buckle formation probability analysis.

The analysis was based on the limit state condition in Equation (10), and by using 108 Monte Carlo simulations. The results indicated in the seventh buckle trigger (worst case from buckle initiation point of view), the probability of buckle initiation failure was less than 10^-4.

Selecting sleeper height

Considering flat rigid seabed, the maximum estimated span length at the vicinity of the pipeline of the buckle triggers was estimated using

Where, E is the pipeline elastic modulus, I the pipeline section moment of inertia, δ the sleeper vertical movement, and w the submerged weight per unit length of the pipeline. This estimation was used as a conservative value for vortex induced vibration analysis of the pipeline.

To calculate the appropriate pipeline span the length, the following were used:

1. To obtain appropriate sleeper behavior, minimum span length of the pipeline aside the buckle triggers considered being at least equal to buckle length aside the sleeper.

2. Pipeline span length aside the buckle trigger shall not cause fatigue damage due to VIV. VIV calculation was based on DNV-RP-F105 using SLTFATFREE software.

Results showed that the sleeper height should be between 0.3 m (1 ft) and 0.6 m (2 ft). This limit was considered for sleeper design.

Analysis of mitigated pipeline

Lateral buckling of the mitigated pipeline was performed to check the final condition of the buckles initiated by the sleepers. To obtain cyclic behavior of the pipeline (pipeline walking), two start-up/shut-down cycles were modeled with pipeline heat-up and cool-down transients, and the effects of hydrodynamic forces. Results showed insignificant changes in pipeline strain due to pipeline walking and hydrodynamic loads.

From finite element analysis, maximum strain in the pipeline after mitigation was about 1%, which was less the 1.5% limit set by low cycle fatigue analysis. •

Acknowledgments

The authors express their appreciation to PETRONAS for supporting this work and permission to use the project data, as its first HP/HT pipeline in the region.

References

1. Submarine Pipeline Systems, DNV-OS-F101, 2006.

2. In-Service Buckling of Heated Pipelines, Hobbs. E., International Journal of Transportation Engineering, vol. 110, No. 2, 1984.

3. HOTPIPE JIP, Design Guidelines for HP/HT Pipelines, L. Collberg et al. Proceeding of OMAE 2005.

4. Design Guidelines for HP/HT Pipelines, S. Goplen et al.

5. Load and Resistance Modeling of the Penguins Pipe-In-Pipe Flowline Under Lateral Buckling, M. Carr, et al., Proceeding OMAE 2004.

6. Penguins Flow Line Lateral Buckling Formation Analysis and Verification, I. Matheson, et al., Proceeding OMAE 2004.

7. Design Strategies for Controlling Lateral Buckling and Axial Creep of HP/HT Subsea Pipelines Installed on a Flat Seabed, K. Torens, N. Kristiansen, Petromin Pipeliner, May 2005.

8. HT/HP Pipe-in-Pipe Snaked Lay Technology, Industry Challenges, J. Hooper, et al., proceeding of OTC 2004.

9. Design of High Temperature/High Pressure (HT/HP) Pipeline against Lateral Buckling, L. Kien, et al.

10. Pipe-Soil Interaction Behavior during Lateral Buckling, Including Large Amplitude Cyclic Displacement Tests by the SAFEBUCK JIP, D. Burton, et al., Proceeding of OTC 2006.

11. Lateral Buckling and Walking, a Challenges for Hot Pipelines, Carr M., et al, Offshore Pipeline Technology, 2003, Amsterdam.

12. The Safe Design of Hot On-Bottom Pipelines with Lateral Buckling Using the Design Guideline Developed by the SAFEBUCK Joint Industry Project, Bruton D., et al, Deep Offshore Technology Conference, 2005, Brazil.

13. Strain Based Design of Pipeline, 45892GTH, EWI.

14. Fatigue Design of Offshore Steel Structures, DNV-RP-C203, 2006.

15. ABS Guide for Building and Classing Subsea Pipeline Systems and Risers, American Bureau of Shipping, 2001.

16. Guide on methods for assessing the acceptability of flaws in metallic structures – BS 7910:1999.

17. ABAQUS 6.6-5 User Manual.

18. Free Spanning of Pipelines, DNV-RP-F105, 2006.

19. Weld Crack Assessment in API X65 Pipeline: Failure Assessment Diagrams with Variations in Representative Mechanical Properties, Lee J. S. et al, Material Science and Engineering, A 373, pp. 122-130, 2004.

20. Time-Dependent Pipe-Soil Resistance for Soft Clay, Brennodden H., et al, Proceeding of OTC 1992.