Simple solutions for downslope pipeline walking on elastic-perfectly-plastic soils
Introduction
Offshore pipelines are becoming increasingly important as hydrocarbon sources become more difficult to reach. The global stability of these pipelines in response to operational loading is a critical issue for the design of oil and gas projects. Such stability comprises the actions of hydrodynamic loads and the effects of expansion and contraction triggered by the High-Pressure and High-Temperature (HPHT) operational conditions (usually imposed by frontier reservoirs), which both constitute the major focus of geotechnical design for pipelines.
The stability of offshore pipelines is also impacted by the slope of the seabed. New hydrocarbon sources are commonly located in regions with noticeable depth variations, in deep water far from shore. These operational conditions are particularly common in the Gulf of Mexico and Northwest Australia, which are currently in operation, and others that are in development, such as the Brazilian Pre-Salt and the Arctic Area.
Threats to the integrity of offshore pipelines by the combination of HPHT conditions and a sloping seabed were first observed by Tornes et al. (2000). Later, industry-supported research documented many cases of ‘axial creeping’ now known as the ‘Pipeline Walking’, as per Carr et al. (2003).
Four mechanisms have been found to incite pipeline walking, as per Bruton et al. (2010):
- 1.
Tension at the end of the flowline;
- 2.
Thermal transients along the line;
- 3.
Multiphase fluid behaviour during restart operations;
- 4.
Seabed slopes along the pipeline route.
Each of the four mechanisms creates an asymmetry in the profile of Effective Axial Force (EAF). This asymmetry generally results in pipeline walking, by causing unequal pipeline displacements during cycles of loading and unloading. This paper focuses on the fourth mechanism.
When pipelines are subjected to changes in temperature and pressure, pipeline walking can occur. During the Start-Up (SUp) phase, temperature and pressure increments cause the pipelines to expand axially. This expansion is resisted by the pipe-soil interaction forces which results in effective compression of the pipeline. When pipelines are submitted to temperature and pressure reductions in the Shutdown (SDown) phase, effective tension is induced in the pipeline.
For ‘long’ pipelines, the effective compression build up occurs along a sufficient length to induce enough mechanical strain to fully compensate for the thermo-mechanical expansion during the hot stages. For ‘short’ pipelines, the compression build up, due to soil resistance, is not sufficient to fully compensate for the expansion.
When ‘short’ pipelines are located on a sloping seabed and are not anchored, cycles of expansion and contraction may cause the pipelines to move with geometric asymmetries between the start-up and shutdown phases. The sloping seabed generates a component of weight to act parallel with the seabed in a downslope direction.
Even if pipeline walking is not a limit state in itself, it may present several design challenges, which include:
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Overstressing of end connections (and in-line connections);
- •
Loss of tension in a steel catenary riser;
- •
Increased loading leading to lateral buckling;
- •
Route instability (curve pull out);
- •
Need for anchoring mitigation.
Therefore, pipeline walking must be avoided since its consequences may create downtime and environmental risk, as pointed out by Tornes et al. (2000).
It is known that pre-operational phases may influence the soil resistance during the operational lifetime of a pipeline through the pre-operational embedment. As noticed by White et al. (2012), typical pipeline embedments can increase the soil axial resistance by 10–20%. This study considers a range of axial resistance so the results cover the range of conditions that could be created by different values of embedment. In practice, the soil resistance may vary during the pipeline life, in which case the walking rate will also vary as a result of this. The authors would like to clarify that the suggested solutions also apply in cases of varying resistance during the field life requiring only an update on the assessments’ inputs.
In this paper, focusing exclusively on the seabed slope mechanism, the authors develop a new analytical strategy extending the traditional solution, which uses a Rigid-Plastic (RP) soil idealization, to a new set of formulations accounting for the Elastic-Perfectly-Plastic (EP) soil behaviour, which is a simple pipe-soil interaction model (Bruton et al., 2008). A parametric study is developed with the help of a Finite Element Analysis (FEA) set, which will serve as proof for the proposed set of new equations, leading to more realistic walking rate predictions.
Section snippets
Background to pipeline walking
Different papers have been published on pipeline walking in the last two decades. Nearly all publications found on this topic are very site-specific (Carneiro and Castelo, 2011; Jayson et al., 2008), with few exceptions providing generalizations and broad guidance on this issue (Carr et al., 2003; Bruton et al., 2010; Carr et al., 2006).
When the downslope mechanism is taken into consideration the effective axial force plot demonstrates the asymmetry, as referred in Section 1 and shown in Fig. 1
Problem definition
To illustrate the behaviour involved in downslope pipeline walking, the properties of a typical example are given in Table 1. General properties, such as temperature loads and geometric data are in keeping with the values presented in Table 1, to allow the results to be applied more broadly in the future.
Rigid-plastic analytical solutions
The current design practice – in accordance with Carr et al. (2006) – involves three different calculation steps to analytically assess pipeline walking rate under the influence of seabed slope.
The first calculation step assesses the distance between the VASs, Xab,RP, as presented by Fig. 1:
The second calculation step assesses the change in force in the pipeline, ΔSS,RP, between start-up and shutdown phases over the length of the pipeline denoted by Xab,RP:
Finite element analyses methodology
The finite element model used for this paper was a simplified model of a straight pipeline laid on a uniformly sloping seabed using the parameters presented in Table 1.
The pipeline was represented by 5001 nodes connected by 5000 equal Euler Bernoulli beams (B33 elements in Abaqus) representing the 5000m long pipeline. Each element, therefore, is 1m in length.
The pipe-soil interaction was modelled as elastic-perfectly-plastic spring-slider elements connected to each pipeline node. The
Finite element analyses comparison with rigid-plastic solution
Fig. 5 presents the effective axial force responses for the EP Stiff and the Soft fits; while Fig. 6 and Fig. 7 present the δx plots for the EP Stiff Fit and the EP Soft Fit, respectively.
From the rigid-plastic case (Bruton et al., 2010), the zero displacement point is exactly the same as the maximum effective axial force point (Table 3). However, the elastic-perfectly-plastic FE results show that the point of zero displacement no longer coincides with the point of maximum effective axial force.
Xab for elastic-perfectly-plastic soil
The three different values for Xab (Xab,RP, Xab,EP_Stiff and Xab,EP_Soft) are compared to δmob, in Fig. 9, which shows the linear dependence of Xab on δmob. Imagining there is a certain level of mobilisation distance which makes Xab to be equal to zero (and consequently ceases the walking pattern), represented by δnull, which will be given later in this paper, the following linear equation might be written:
Xab,EP for use in equation (4) is now defined for
ΔSS for elastic-perfectly-plastic soil
For rigid-plastic soils, ΔSS can be obtained directly from the basic problem parameters using equation (2). For elastic-perfectly-plastic soils, however, ΔSS is not straight forward, as the effective axial force profile is not triangular. For this reason, the effective axial force equations need to be redefined by adopting the solution for an elastic column compressed within an elastic medium, as used in the analysis of piles. This leads to a second order linear differential equation which
Walking rate for elastic-perfectly-plastic soil
Based on the above expressions, the walking rate for elastic-perfectly-plastic soils can be derived. Taking into account equation (5), the general modifications are:
To validate this revised expression for WREP, a parametric finite element analyses study was conducted.
Finite element analyses parametric study
The parametric study used a range of values for the following parameters:
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Pipeline length;
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Pipeline submerged weight;
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Friction factor;
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Route overall slope.
For these core properties three different values were attributed for each, resulting in 81 different combinations. The different values used are shown in Table 6.
Since the focus of this paper is the influence of axial mobilisation distance, eight different values of δmob were considered, in terms of pipeline steel outside diameter (OD), (0.03OD,
Conclusions & final remarks
This paper provides an analytical solution that solves pipeline walking problems for elastic-perfectly plastic (EP) pipe-soil response, benchmarked and validated against finite element analyses performed with an elastic-perfectly-plastic user-defined element. These revised solutions improve understanding of the parameters involved in elastic-perfectly-plastic soil behaviour for pipeline walking assessment. The paper resolves how the fundamental solution for rigid-plastic pipe-soil interaction
Acknowledgment
This research forms part of the activities of the Centre for Offshore Foundation Systems (COFS), established under the Australian Research Council’s Research Centres Program and currently supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering. The authors acknowledge the support from The University of Western Australia and Shell.
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