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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

EFFECTS OF TOP TENSION ON STRESS UTILIZATION IN PIPE LAYING OPERATIONS: A CASE STUDY FOR BARE PIPE, INSULATED PIPE AND PIPE-IN-PIPE SYSTEMS. Abstract The effects of top tension on stress utilization in pipe laying operations is a key component of pipeline installation design that must be critically analysed and ascertained if pipe laying operations in subsea environment must be successful. Key considerations such as the water depth, pipe weight per unit length, span length, top tension, and environmental conditions of the target subsea environment cannot be over-emphasized. The structural behaviour of the pipe system during installation operation is dependent on both the overall behaviour of the pipeline system, and the mechanism of load transfer between the installation vessel and the pipe, and seabed-pipe interaction at the touch down point (TDP). This paper will illustrate the various methods of pipe laying systems available in the subsea industry and attempts to discuss the modus operandi for each. Key catenary equations for the pipe laying systems were also derived in relation to analysing the various force components acting on the pipeline system during its installation. In this light, case studies for three different pipeline configuration (Bare, Insulated and Pipe-in-Pipe Pipeline Systems) common in the industry were considered in relation to analysing and comparing the effects of hoop, bending and axial stresses at the TDP due to the applied top tension at the surface from the installation vessel at different top tension ratio. It concludes by presenting the stress utilization curve (SUC) as a function of the top tension ratio for each of the pipe system being studied in lieu to exposing the effect of stress utilization for each of the pipeline during laying operations. Based on these studies, a few significant conclusions are drawn, providing the design and installation monitoring of deepwater pipeline with theoretical basis. Key Words: Stress Utilization, Top Tension, Ramp Angle, Span Length, Bare Pipe, Insulated Pipe, Pipe-In-Pipe, Catenary

1.0 Introduction In recent decades, the increasing demand for energy has led to a rapid development of subsea and offshore assets for Oil & Gas Exploration and Production (E&P). It is crystal clear that the era of “easy oil” is over! As operating conditions become stern, high performance subsea pipelines with superb reliability attributes is required to facilitate long-term production of the hydrocarbon from the reservoir to the production platform at the surface. As operators take the bull by the horn to develop these subsea fields located in extremely harsh environment and operating conditions, new challenges have been created in design and installation of subsea pipelines. The creation of these challenges has spurred the O & G operators over the years to develop novel approaches for pipeline design and installation. Some of the most popular methodology, tools and techniques been utilized in the industry today to install pipelines in unbenign environment are the J-Lay, S-Lay, Reel Lay and the Towed Pipe Laying Systems. Each of these pipe laying systems will be discussed in the next section and conscious efforts will be made towards deriving the catenary equations using a catenary model for subsea pipeline installation applicable for the S-Lay, J-Lay and Reel Lay laying systems. Depending on the catenary configuration of the pipeline during its installation, there are a number of stresses introduced intentionally and un-intentionally in order to ensure a successful installation operation. Thus, the design of the subsea pipeline must ensure that its curvature remains well within elastic limits during its storage, transportation and installation, and that fatigue damage remains acceptable during its entire service and design life. The derived catenary equations will be used to model the effect of top tension on stress utilization for the three pipe configuration under consideration. The analysis will be done based on an installation depth of 2, 600 meters (8,530 feet) which is typically deepwater while assuming a rigid and frictionless seabed. In addition, the effects of external forces such as waves and current is assumed to be negligible for the field under study. The pipe system is also assumed to be a no flood situation and thus will be modeled to be empty for the stress utilization analysis. [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

2.0 Pipe Laying Systems Each method of pipe laying systems has its own application which is dependent on pipe size, water depth, and specific project requirements. As a result the overall efficiency of pipelay operations is not simply related to the rate at which the vessel can lay pipe, but a combination of the lay rate together with the efficiency of the vessel to install structures as part of the pipeline [1]. This section will discuss briefly the main pipe laying systems available in the industry. 2.1 S-Lay Pipe Laying Systems The most common method of pipeline installation in shallow water is the S-lay pipe laying system. It has two important devices: stinger and tensioner. Stinger controls the overbend of pipeline. Its geometry, length, and curvature, are the function of water depth, lay tension requirement and geometry and material of the pipeline [2]. The tensioners on the vessel/barge pull on the pipeline, keeping the whole section to the seabed in tension. The reaction of this pull is taken up by anchors installed ahead of the barge or, in the case of a Figure 1: S-Lay Pipe Laying System [4] dynamically positioned (DP) vessel, by thrusters. These barges/vessels are fitted with tension machines, abandonment and recovery (A&R) winches, and pipe handling cranes [3]. The major aspects of pipeline design which influences the suitability of the S-Lay method are pipe diameter, maximum water depth and submerged weight. The S-Lay vessel consists of several work stations which carries out firing line operations such as the welding, inspection and coating. Along the firing line, the pipes are welded, coated and tested horizontally. The welded pipe strings is then passed through the stinger suspended from the back of barge into water in nearly a vertical slope which is in turn finally laid on the seabed. The configuration of the pipeline during laying process resembles “S”, and it is divided into the overbend on stinger and the sagbend from lift-off point to touch down point on the seabed, as shown in Fig. 1. The curvature of the overbend is controlled by 6 to 14 rollers installed on the stinger. The rollers are normally spaced in 5 to 10 m. The sagbend curvature is controlled by tension at the tensioner on the lay-barge. For deep and ultra -deep water installations, large tension and high curvature stinger are required in order to achieve the nearly vertical departure. However, such setup can lead to large plastic deformation in overbend area. The S-Lay system has the ability to lay both in shallow and deep water. Pipe laying in deepwater can be achieved by adopting a form of Steep S-Lay by setting the lift off point of the pipe from the stinger as near vertical as possible. However, to keep the size of the stinger to a reasonable size, the curvature has to be increased. This will result to higher strains in the pipe wall in the overbend area as high as 0.45% which is higher than the required specification of 0.20% for pipeline overbend (stinger) and 0.15% for pipeline sagbend (spanning section) in accordance with the Statoil Specification F-SD-101 [4, p. 606]. The S-lay methods are much more appropriate from the pipeline fabrication point of view, and appear as a better option for the laying of relative long lines such as gas trunk line or long tie back.

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

2.2 J-Lay Pipe Laying Systems To keep up with the discovery of deepwater oil and gas fields, the J-lay system for pipeline installation was invented. The J-Lay technique was originally considered over conventional S-Lay techniques in order to minimize the extreme lay tensions required in deepwater in addition to the excessive strains generated in the overbend area. Consequently, the water depth limitation of the S-Lay system has led to the development and adoption of the J-Lay system as a prime technique of laying pipeline in ultra-deep water. As shown in Figure 2: The J-Lay Pipe Laying Vessel Configuration Fig.2, the J-Lay method allows the installation of the pipeline through a vertical or near vertical ramp (typically within 80° to 90°) positioned on board of a vessel. This configuration facilitates the installation of the pipe at water depths beyond the limits of the S-Lay system [5]. The J-Lay method involves welding the pipeline together from a series of joints in the vertical position using one welding work station. The pipeline is maintained in the optimal angular position and pulled under a predetermined high tensile force while being lowered to the seabed. The J-Tower is the core part of the J-Lay system with the main components being similar across all the barges/vessels. An erector arm is used to bring the pipe stalk up the vertical tower where it is held in the tower by an elevator system (Fig.3). Once the welded joint has been completed, the elevator lowers the complete string down to the working table and the process begins again [1, p. 5]. Pinned to the tower support structure, the stinger extends approximately 50 feet below the water surface and supports three (3) hydraulically operated, retractable full encirclement roller assemblies designed to support the upper portion of the pipeline during pipeline welding operations. The A-frame and foundation is a single piece module whose function is to provide support to the other major components of the J-Lay System. It is comprised of tubular frames supported by large boxed girders. The A-frame and Figure 3: J-Lay Pipe Laying System foundation extends over the starboard side of the vessel approximately 20 - 30 feet enabling the pipeline centreline to be located outboard of the vessel for J-Lay operations. Weighing approximately 450 tons and the largest single component of the J-Lay System, the A-frame and foundation supports all of the ancillary hydraulic pumps, hoists, and control systems necessary to operate the major J-Lay System components. Surface diving equipment and NDT facilities are also located on the foundation [6]. The pipeline from the surface to the seabed is one large radius bend resulting in lower stresses than an S-lay system in the same water depth. There is no over-bend, and a large stinger required in S-lay to support the pipe in deepwater is eliminated. The horizontal forces required to maintain this configuration are much smaller than required for an S-lay system. This lends itself for DP shipshape vessels and derrick barges to be equipped with [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

a J-lay tower. On a general note, the lay rate for the J-Lay vessel increases with the stalk length. Large J-Lay systems can deal with stalks made up from four to six standard pipe lengths (48 m to 72 m); consequently, these are very large tower systems requiring very large vessels. One of the challenge of a J-Lay system is having to perform the process of welding, nondestructive testing, and corrosion coating at one work station as opposed to the S-Lay process which performs tasks simultaneously in multiple work stations [7]. The J -Lay method appears as a natural configuration from the catenary point of view and is much more appropriate to the installation of in line structures. 2.3 Reel Lay Pipe Laying Systems Reel pipelay is a method of installing pipelines in the ocean from a giant reel mounted on an offshore vessel. Pipelines are assembled at an onshore spool-base facility and spooled onto a reel which is mounted on the deck of a pipelay barge [3]. The reel ship Apache is a notable name in the development of the Reel – Lay pipe laying technology. It was first operated in 1979 when it was used in the Pipeline Under the Ocean (PLUTO) project across the English Channel [8]. The reeling method, which can be considered from a pipe laying configuration point of Figure 4: Reel Lay Pipe Laying System view as a subset of J-Lay, can prove to be a useful solution where high integrity welding is required. One of the main point of attraction for this system is that the pipeline is welded into stalks around 1km in length onshore and then wound onto the reel of the pipelay ship. Consequently there is less time pressure on the welding operations compared to offshore construction, allowing the selection of an improved fatigue class of stress (S) against the number of cycles to failure (N) - S-N curve with a potentially small cost impact. However the influence of the plastic bending involved in the reeling process will need to be considered in the overall weld acceptance criteria. In addition the reeling technique is only suitable for relatively small diameter flowlines (18 inches max), which has a spool base close to the offshore field [1, p. 3]. The pipe is stowed in a vertical reel. The pipe reel is mounted in a reel well amidships with horizontal axis transverse to the ship’s centreline. In order to drive the reel for spooling during loading or pipe recovery, a considerable amount of electrical power must be provided by the ship’s generators. Some of this power is also used to position pipe straightening and de-ovaling machinery vertically and transversely. The pipe-laying operation is controlled from a control room affording a clear view of the pipe from the reel to the point where it enters the water, aft of the ship. During the pipe-laying operation, the vessel is conned and navigated from the control room, which has a 360 degree view. The vessel is also equipped with bow thrusters to assist in course and station keeping during lay operation [9, p. 4]. The primary advantage of the Reel-Lay System is attributed to the speed with which the pipe can be discharged at sea. This is due to the patented technique of straightening the pipe during unspooling and discharging operations. In addition, the Reel-Lay System has the advantage of being able to discharge pipe in very deep waters where it is extremely difficult and/or impossible for conventional welding barges to operate [9, p. 2]. This advantage stems from the peculiar geometry of the ship which allows the pipe to enter the [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

water at very steep angles (up to 50°) while conventional lay systems are limited to about a 15° entry angle. This also allows the Reel-Ship to work without a stinger, which are required by conventional lay systems. Reel - Lay offers a cost effective offshore installation method for high strength steel pipe [10]. 2.4 Towed Pipe Laying Systems The towed pipe laying system is a special technique deployed for installing pipeline bundles. A pipeline bundle is a carrier pipe within which any combination of individual pipelines and umbilical components is carried [11]. As shown in figure 5, typical pipe bundle system may consist of production flowlines which could be 6'' to 8'' in diameter, with a test line, 4'' to 6'' in diameter. Other sub-components can be Figure 5: Pipe Bundle System

methanol/chemical injection lines probably 2'' to 2⅔'' in diameter, control/instrumentation umbilical and possibly heat tracing/direct electrical heating lines [12, p. 1]. In addition, the internal production flowlines may be insulated with syntactic material or gel. This whole system is then enclosed in a carrier pipe, typically 24'' to 36'' in diameter. The individual components terminate in “Towheads” which is a component in the system within which manifolding may take place. Consequently, the complete bundle system becomes very complex for S-Lay, J-Lay or Reel Lay pipe laying operations. Owing to this fact, the towed pipe laying system becomes a suitable methodology to install the bundle pipeline system in order to facilitate low stress installation loads on the pipe wall. As shown in figure 6, there are four (4) tow methods deployed for the installation of pipe bundles which are described in the subsection below;

Figure 6: Towed Pipe Laying Systems

2.4.1 Surface Tow As shown in figure 6a, the surface tow method utilizes buoyancy modules/tanks to facilitate the floatation of the pipeline close to the mean water level (MWL) thus avoiding all seabed contact during towing. However, one of the significant disadvantages of this technique is the impact of surface waves and current making it sensitive to fatigue during logistics and installation operation. Consequently, its use in deep water and long offshore pipeline is limited [13, p. 2]. 2.4.2 Controlled Depth Tow As shown in figure 6b, the controlled depth tow technique is a towing system that combines the advantages of off-seabed and surface tow techniques. It is most suitable for the transportation of bundles to very congested seabed. In this method, the bundle pipe to be transported is encased in a carrier pipe. The carrier pipe has chains (figure 7) attached to it at 7: Carrier Pipe intervals along its length to assist in the control of buoyancy during Figure with Chains Attached [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

transportation [13, p. 2]. When stationary, the bundle is maintained at a constant height above the seabed due to the chains. As it sinks, more chain links are supported by the seabed until the system is in equilibrium. When in motion, the chains develop drag forces and adopt an inclined angle opposite to the direction of tow. The change in the chain’s centre of gravity along with hydrodynamic lift forces the chains reduces the submerged weight of the system causing the bundle to rise in the water column allowing it be towed free of the seabed but also at a depth free from the influence of surface waves and currents. The higher the tow speed, the higher the bundle flies [14, p. 12, 15, p. 25]. 2.4.3 Off-Seabed Tow As shown in figure 6c, this technique relates to towing the bundle at a fixed depth above the seabed. Similar to the controlled depth technique, the desired depth is achieved by a combination of buoyancy tanks and free hanging chains attached to the carrier pipe (Figure 8). The chains are constantly in contact with the seabed. Thus, before pipe towing to the field commences, the seabed along the route for towing is pre-surveyed in order to ensure it is free 8: Carrier Pipe from obstacles that might hinder a successful journey to its target Figure with Buoyancy and destination. Consequently, this technique is most suitable for towing Chains Attached along seabed route free from obstacles [15, p. 25]. 2.4.4 Seabed Tow As depicted in figure 6d and as the name suggests, the seabed tow technique require the bundle to be in contact with the seabed during tow to the field. Similar to the off-seabed tow, this technique requires the selection of a tow route clear of seabed obstacles and is therefore more suited to fields where subsea infrastructure is limited in development. For heavy bundles, on-bottom weight of the reduced either by incorporating buoyancy modules or by use of large carries pipes [13, p. 1]. 3.0 Limitations and Comparison of Pipe Laying Systems Table 1 below shows a comprehensive comparison of the pipe laying systems for subsea applications. Table 1: Comparison of Pipe Laying Systems for Subsea Applications

S/N

1

2

3

Attributes

Operating Environment

Efficiency/ Installation Rates

Versatility & Flexibility

S-Lay  Most suitable for shallow water. However, stinger tip can be reconfigured to accommodate installation in middeep water. (approx.. 700 m)  Typical lay rate using single joint operations are 1.5 to 2.5 km/day. Higher lay rate can be achieved using double or triple joint operation.  Restrictions for horizontal tension and departure angle. As water depth increases, pipe lay rate decreases.

 





 

Pipe Laying Systems J-Lay Reel Lay Most suitable for laying  Suitable for pipe pipeline in deep water laying environment. operations in Adversely affected by deep water for environmental limits due depths up to to wind, wave and 3000 m. currents. Thus, requiring  Take advantage more top tension of short weather capacity. windows. Lay rate is determined by  Average pipelay the geometric properties of about 20 of pipe (diameter and km/day. wall thickness) to be laid. However, lay Typical lay rate using vessel will have single joint operation for to return to smaller pipe diameters spool base for are between 3.5 to 4 reloading km/day. Reduced stinger length  Limitation on when compared to the Sinstallable pipe Lay method. diameter. Has a limitation for Generally not installable diameter at greater than 16''. certain depths.

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

Towed  Suitable for pipe laying operations in deep water for depths up to 1000 m.  Ideal for pipe lay on crowded sea bed.  Faster and cheaper than other methods of pipe laying as cost of employing the services of large lay vessels is eliminated.  Testing and commissioning of complete system offshore thus reducing offshore time. Page 7

Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

4.0 Catenary Modelling For Tension, Stress and Strain of Subsea Pipeline Installation As depicted in figure 9, during installation, a pipeline will exhibit large deflection from its stress state when under the influence of tension and its own weight. Consequently, along the curvature of the pipeline, the sagbend is governed by the applied axial tension. The catenary model as shown in figure 9 will be used to establish the relationship between axial tension and curvature of the pipeline. For this task, the flexural rigidity of the pipeline will be ignored Y in the catenary model calculation. There are two main tension components Figure 9: The Catenary Model for Subsea Pipeline Installation [4, p. 609] acting on the pipeline during installation. These force components are;  Horizontal Component of Tension (𝑻𝒉 ): This is the constant force acting from the point where the pipeline touches the seabed (TDP) and up to the stinger tip on the installation vessel.  Vertical Component of Tension (𝑻𝒗 ): This is the force that increases from the touch down point (TDP) on the seabed and up to the stinger, because of the submerged weight of the suspended part (sagbend) of the pipeline. As mentioned earlier some of the key assumptions made in the derivation of the equations for the catenary model in figure 9 are;  The flexural rigidity of the pipeline is not considered which leads to the likelihood that the horizontal and vertical components of tension is over estimated.  The effects of sea current velocity and surface waves on the pipe wall is negligible.  The effects of sea temperature has negligible impact on the pipe wall during installation. From Figure 9 and the simplified force component diagram in figure 10, the relationship between the horizontal component of tension (𝑇ℎ ), vertical component of tension (𝑇𝑣 ) and submerged weight of the pipeline (𝑤𝑠 𝑠 ) can be expressed as; (4.1) 𝑇ℎ = 𝑇𝑣 cos 𝜃 Similarly; 𝑇𝑣 sin 𝜃 = 𝑤𝑠 ∗ 𝑠

(4.2) Figure 10: Simplified Force Component Diagram

Where; 𝑤𝑠 − 𝑆𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒𝑙𝑖𝑛𝑒 (𝑁/𝑚) 𝑠 − 𝑇ℎ𝑒 𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑠𝑒𝑎𝑏𝑒𝑑 𝑡𝑜 𝑡ℎ𝑒 𝑠𝑡𝑖𝑛𝑔𝑒𝑟 𝑡𝑖𝑝 𝑖𝑛 𝑡ℎ𝑒 𝑌 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 (𝑚) 𝜃 − 𝐴𝑛𝑔𝑙𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑋 − 𝐴𝑥𝑖𝑠 Similarly, 𝑇ℎ =

𝑤𝑠 𝑠 tan 𝜃

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

(4.3) Page 8

Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

At the vertical component, 𝑇𝑣 = 𝑤𝑠 𝑠. Hence equation 3 can be rewritten as; 𝑇𝑣 tan 𝜃 = (4.4) 𝑇ℎ For completeness, the general catenary equations is stated below [4, p. 609]; 𝑇ℎ 𝑥𝑠 𝑤𝑠 𝑦= (cosh − 1) (4.5) 𝑤𝑠 𝑇ℎ Where; 𝑦 − 𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑆𝑡𝑖𝑛𝑔𝑒𝑟 𝑇𝑖𝑝 𝑎𝑏𝑜𝑣𝑒 𝑠𝑒𝑎 𝑏𝑒𝑑 (𝑚) 𝑥𝑠 − 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑇𝐷𝑃 𝑡𝑜 𝑡ℎ𝑒 𝑆𝑡𝑖𝑛𝑔𝑒𝑟 𝑇𝑖𝑝 (𝑚) The horizontal distance between the TDP and stinger tip can also be expressed as; 𝑇ℎ 𝑥𝑠 = ∙ sinh−1 (tan 𝜃) (4.6) 𝑤𝑠 The curvature of the pipe at the sagbend region during installation can also be expressed as; 𝑑𝜃 𝑑2 𝑦 𝑤𝑠 𝑥𝑠 𝑤𝑠 = 2 cos 𝜃 = cosh ( ) cos 𝜃 𝑑𝑠 𝑑𝑥 𝑇ℎ 𝑇ℎ The greatest curvature is at the TDP and can be expressed as; 1 𝑤𝑠 = =𝑐 𝑅 𝑇ℎ

(4.7)

(4.8)

Where; 𝑅 − 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑅𝑎𝑑𝑖𝑢𝑠 𝑎𝑡 𝑇𝐷𝑃 (𝑚) 𝑐 − 𝐶𝑢𝑟𝑣𝑎𝑡𝑢𝑟𝑒 (𝑚−1 ) As mentioned earlier, the length of the suspended part of the pipeline is represented by 𝑠 and can be expressed as; 𝑠 = 𝑦√1 + 2

𝑇ℎ 𝑦𝑤𝑠

(4.9)

Combining equation 4 and 9, the horizontal force component can be expressed in terms of 𝜃,𝑤𝑠 , and 𝑦 as; 𝑇ℎ =

𝑦𝑤𝑠 (1 + √1 + 𝑡𝑎𝑛2 𝜃) 𝑡𝑎𝑛2 𝜃

(4.10)

It is noteworthy that in deep water it is reasonable to say that the departure angle, from stinger tip and the angle in the inflection point are approximately the same. Since the location of the inflection point are unknown, the horizontal tension 𝑇ℎ can be estimated using equation 10 by using the departure angle and height above seabed at the stinger tip [4, p. 610]. The pipeline is subjected to three principal stresses during its installation. These are;  Bending Stress, 𝝈𝒃 : This is stress that occurs as a result of the curvature of the submerged pipe. The bending stress is a major contributor of the stress state in the pipe during installation operation. The bending stress is tensile on the convex side (upper fiber) and compressive on the concave side (lower fiber) of the bend. The maximum [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

bending stress around the curvature of a submerged pipe during pipe lay can be expressed as; 𝐷𝑜 𝜎𝑏 = ±𝐸 (4.11) 2𝑅 Where; 𝐸 − 𝑌𝑜𝑢𝑛𝑔 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑃𝑖𝑝𝑒𝑙𝑖𝑛𝑒 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 − 𝑆𝑡𝑒𝑒𝑙 (207 × 109 𝑃𝑎) 𝐷𝑜 − 𝑂𝑢𝑡𝑒𝑟 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑃𝑖𝑝𝑒𝑙𝑖𝑛𝑒 (𝑚) 

Axial Stress, 𝝈𝒂 : This is the stress directed longitudinally along the pipe wall as a result of the tension applied in the vertical axis, 𝑇𝑣 by the tensioner on the lay vessel. The axial stress at the TDP can be expressed as; 𝐹𝑎 𝜎𝑎 = (4.12) 𝐴𝑠 𝐹𝑎 = 𝑇𝑣 − 𝑤𝑠 𝑑 − 1⁄4 𝑃ℎ 𝜋(𝐷𝑜 + 2𝑡𝑖 )2 (4.13) Where; 𝑃ℎ − 𝐻𝑦𝑑𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑃𝑎) 𝑡𝑖 − 𝐼𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 (𝑚) 𝐴𝑠 − 𝐶𝑟𝑜𝑠𝑠 𝑆𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑡𝑒𝑒𝑙 𝑤𝑎𝑙𝑙 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑃𝑖𝑝𝑒𝑙𝑖𝑛𝑒 (𝑚2) 𝑑 − 𝑊𝑎𝑡𝑒𝑟 𝐷𝑒𝑝𝑡ℎ (𝑚) The longitudinal stress 𝜎𝑙 which is a corollary to the axial stress and the bending stress can be expressed as; 𝜎𝑙 = 𝜎𝑎 ± 𝜎𝑏 (4.14) Where; 𝜎𝑙𝑢 = 𝜎𝑎 + 𝜎𝑏 (𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑛𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠 @ 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑓𝑖𝑏𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒) (4.14𝑎) 𝑙 𝜎𝑙 = 𝜎𝑎 − 𝜎𝑏 (𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑛𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠 @ 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑓𝑖𝑏𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒) (4.14𝑏)



Hoop Stress, 𝝈𝒉 : This is the stress occurring circumferentially on the pipe wall. It acts to “hold” the pipe wall together and acts as the primary component that resists pressure loading. For a bare line pipe, the hydrostatic pressure acts on the outer surface of the pipe and produces compressive hoop stress which can be expressed as; 𝐷𝑜 𝜎ℎ = −𝑃ℎ (4.15) 2𝑡𝑠 Where 𝑡𝑠 𝑡ℎ𝑒 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑡𝑒𝑒𝑙 𝑤𝑎𝑙𝑙 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 (𝑚) The hydrostatic pressure, P can be calculated as; 𝑃ℎ = 𝜌𝑤 𝑔(𝑑 − 𝑦) (4.16) Where; 𝜌𝑤 − 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑆𝑒𝑎𝑤𝑎𝑡𝑒𝑟 (1,025 𝑘𝑔⁄𝑚3 ) 𝑔 − 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝐺𝑟𝑎𝑣𝑖𝑡𝑦 (9.81 𝑚⁄𝑠 2 ) Since the maximum hoop stress is at the TDP, then y = 0. The von Mises yield stress criterion is considered to be a safe deterministic approach for design engineers to check the reliability of a material when subjected to various loads under installation and operating conditions. Using this information, an engineer can determine if his design will fail or not. The equivalent von Mises Stress, σe is calculated by combining the three principal stresses experienced by the pipeline during its installation. It can be expressed as;

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

σe = √(𝜎𝑎 − 𝜎𝑏 )2 + 𝜎ℎ 2 − (𝜎𝑎 + 𝜎𝑏 )𝜎ℎ

(4.17)

Or, in terms of the longitudinal stresses; 2 𝜎𝑒𝑢 = √𝜎𝑙𝑢 + 𝜎ℎ 2 − 𝜎𝑙𝑢 𝜎ℎ (𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 @ 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑓𝑖𝑏𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒) (4.17𝑎) 2

𝜎𝑙𝑙 = √𝜎𝑙𝑙 + 𝜎ℎ 2 − 𝜎𝑙𝑙 𝜎ℎ (𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 @ 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑓𝑖𝑏𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒) (4.17𝑏) If the maximum value of von Mises or equivalent stress induced in the pipe wall is more than its uniaxial yield strength σy during installation, failure of the pipe wall by buckling is likely to occur. Consequently, the stress utilization, S.U is used to measure the level of safety from failure for the pipe during lay operations and can be expressed as; 𝑀𝑎𝑥(𝜎𝑒𝑢 , 𝜎𝑒𝑙 ) 𝑆. 𝑈 = ≤ 100% (4.18) 𝜎𝑦 As shown in equation 17, to prevent failure by buckling, the stress utilization factor (S.U) must be less than 1.

5.0 Stress Utilization Analysis: Case Studies The safety of offshore pipelines in complicated loading conditions such as high ambient pressure, axial tension and bending moment during deepwater installation has drawn more attentions than shallow waters [16]. This present section is focused on the mechanical analysis of bare, insulated and pipe-in-pipe pipe systems using S-lay laying method from a lay barge over the stinger to the seabed. The effects of laying parameters such as the tension of top end of pipeline, the stinger radius, the pipe diameter and wallthickness on the mechanical behaviour of the pipeline are analysed using the basic catenary equation derived in the previous section. 5.1 Case 1: Bare Pipe Let us consider a simple bare line pipe shown in figure 10 with the following mechanical and physical properties shown in table 2;

Figure 10: Bare Pipe

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems Table 2: Pipe and Environmental Data for Bare Pipe Case Study Parameters Water Depth Density of Seawater

Environmental Data Symbols Value d 2,600.00 ρw 1,025.00

Acc. due to Gravity

g

S.I Units m 3 kg/m m/s2

9.81

Bare Pipe Data Symbols Value Steel X65 σy 448,159,223.21 E 2.07E+11 ρs 7,850.00 Do 0.3239 tp 0.0159 Di 0.2921

Parameters Material Type Grade Yield Strength Young's Modulus Density of Steel Pipe Outer Diameter Pipe Wall Thickness Pipe Inner Diameter

S.I Units NA NA Pa Pa kg/m3 m m m

Pipe Geometric Properties Symbols Value Ah Hydrodynamic Area 0.0824 Parameters

Pipe Internal Area

Ai

0.0670

Area of Steel Pipe Submerged Weight

As Ws

0.0154 356.2532

S.I Units 2

m m2 m2 N/m

An excel spreadsheet was set up to calculate the resulting principal stresses and stress utilization using the formulas presented from equations 4.1 through to 4.18. Guess estimate of top tension ratio was used to carry out a sensitivity analysis as to how the pipe will respond mechanically at different top tension ratios. The results of stress utilization and top tension ratio was plotted and the resulting curve is shown in figure 12. Figure 11 below is a screen snapshot of the excel file used in performing the calculation. Please see appendix II containing the excel commands/syntax used in carrying out the calculation. As shown in table 2, the bare pipe’s submerged weight was calculated by; 𝑤𝑠 = [(𝜌𝑠 × 𝐴𝑠 ) − (𝜌𝑤 × 𝐴ℎ )]𝑔 (5.1) Principal Stresses | von. Mises Stress | Stress Utilization Parameters

Referenced Equation

Symbols

S.I Units

Top Tension Tension @ TDP

Tv Th

Angle of Inflection

θ

Hor. Dist TDP Arc Length Curvature Bending Radius Bending Stress Axial Force Axial Stress

x s c R σb Fa σa

Longitudinal Stress

σl

Hydrostatic Pressure Hoop Stress

Ph σh

N N Radians Degrees m m per m m Pa Pa Pa Upper Fibre: Pa Lower Fibre: Pa Pa Pa Upper Fibre: Pa

4.6 4.9 4.8 4.8 4.11 4.12 4.13 4.14a 4.14b 4.16 4.15 14.17a

σe

Lower Fibre: Pa

14.17b

S.U

Pa %

4.18

von Mises Equi. Stress Max von Mises Equi. Stress Stress Utilization

4.1

Guess Estimates of Top Tension Ratio 1.2 1.3 1.4

1.1 1,018,884.15 92,625.83 1.48 84.78 803.13 2,848.16 0.0038 260.00 128,937,115.38 - 2,061,534.37 - 133,996,318.49 - 5,059,203.10 - 262,933,433.87 26,143,650.00 - 266,287,051.42

1,111,509.98 185,251.66 1.40 80.41 1,288.50 3,076.36 0.0019 520.00 64,468,557.69 - 1,968,908.54 - 127,975,792.90 - 63,507,235.20 - 192,444,350.59 26,143,650.00 - 266,287,051.42

263,793,838.08 264,626,180.82

240,895,845.27 238,113,802.93

264,626,180.82 240,895,845.27 59.05% 53.75%

-

1.5

1,204,135.81 277,877.49 1.34 77.01 1,694.58 3,380.00 0.0013 780.00 42,979,038.46 1,876,282.71 121,955,267.30 78,976,228.84 164,934,305.77 26,143,650.00 266,287,051.42

1,296,761.64 370,503.33 1.28 73.40 2,001.84 3,488.27 0.0010 1,040.00 32,234,278.85 - 1,783,656.88 - 115,934,741.71 - 83,700,462.87 - 148,169,020.56 26,143,650.00 - 266,287,051.42

1,389,387.47 463,129.16 1.23 70.53 2,291.57 3,676.96 0.0008 1,300.00 25,787,423.08 - 1,691,031.04 - 109,914,216.12 - 84,126,793.04 - 135,701,639.20 26,143,650.00 - 266,287,051.42

236,887,507.82 232,792,287.27

235,852,097.25 231,100,326.28

235,763,091.67 230,625,539.04

236,887,507.82 52.86%

235,852,097.25 52.63%

235,763,091.67 52.61%

Figure 11: Screen Snapshot of Detailed Analysis for Bare Pipe Stress Utilization Analysis (2,600 m Water Depth)

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Figure 12: Plot of Stress Utilization versus Guess Estimates of Top Tension Ratio for Bare Pipe (2,600 m Water Depth)

As shown in figure 12 above, it can be concluded that the bare pipe will not fail during installation as the stress utilization for the various top tension ratio considered is less than 1 (i.e. 100%). 5.2 Case 2: Insulated Pipe The driving phenomena for deep water pipelines have drastically evolved over the last ten years with the development of deep water fields. The key driver for the design of the field layout and the flowlines is undoubtedly the flow assurance of multiphase fluids. This has led to a significant increase of insulated flowlines, which has had a great impact on the overall behavior of pipelines on the sea bed. The use of wet insulation materials such as polypropylene and polyurethane has resulted in a general reduction in the submerged weight of production flowlines, this in combination with the very soft soil conditions found in deep water locations has led to the significant increase in pipeline movements induced by pressure and temperature of the internal fluids. Let us consider a simple wet insulation pipe configuration system shown in figure 13 with geometric and physical properties highlighted in table 3.

Figure 13: Wet Insulated Pipe

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems Table 3: Pipe Data for Insulated Pipe Case Study (2,600 m Water Depth)

Insulated Pipe Data Symbols Value Steel X65 σy 448,159,223.21 E 2.07E+11 ρs 7,850.00

Parameters Material Type Grade Yield Strength Young's Modulus Density of Steel

S.I Units NA NA Pa Pa kg/m3

850.00 0.3239 0.0159 0.2921

kg/m3 m m m

0.4239 0.0500

m m

Insulation Inner Diameter Diin 0.3239 Pipe Geometric Properties Parameters Symbols Value Ah Hydrodynamic Area 0.1411 Pipe Internal Area Ai 0.0670

m

Density of Insulation Pipe Outer Diameter Pipe Wall Thickness Pipe Inner Diameter

ρin Do tp Di

Insulation Outer Diameter Insulation Thickness

Do ti

in

S.I Units m2 m2 2

Pipe External Area

Ao

0.0824

m

Area of Steel

As

0.0154

m

Area of Insulation Pipe Submerged Weight

Ain Ws

0.0587 255.4249

2

m2 N/m

Using the same environmental data and guess estimates of top tension requirement from the previous analysis carried out for bare pipe, the stress utilization analysis was performed for the insulated pipe. Figure 14 shows a screen snapshot of the results with more details on the excel commands used to execute the calculations presented in appendix III. As can be seen from table 3, the insulated pipe’s submerged weight was calculated by; 𝑤𝑠 = [(𝜌𝑠 × 𝐴𝑠 ) + (𝜌𝑖𝑛 × 𝐴𝑖𝑛 ) − (𝜌𝑤 × 𝐴ℎ )]𝑔 (5.2)

Principal Stresses | von. Mises Stress | Stress Utilization Parameters

Referenced Equation

Symbols

S.I Units

Top Tension Tension @ TDP

Tv Th

Angle of Inflection

θ

Hor. Dist TDP Arc Length Curvature Bending Radius Bending Stress

4.6 4.9 4.8 4.8 4.11

Axial Force

x s c R σb Fa

N N Radians Degrees m m per m m Pa Pa

4.12

Axial Stress

σa

Longitudinal Stress

σl

Hydrostatic Pressure Hoop Stress

Ph σh

Pa Upper Fibre: Pa Lower Fibre: Pa Pa Pa Upper Fibre: Pa Lower Fibre: Pa Pa %

4.13 4.14a 4.14b 4.16 4.15 14.17a 14.17b

von Mises Equi. Stress Max von Mises Equi. Stress Stress Utilization

σe S.U

4.1

4.18

Guess Estimates of Top Tension Ratio 1.2 1.3 1.4

1.1

1.5

730,515.24 66,410.48 1.48 84.78 803.13 2,848.16 0.0038 260.00 128,937,115.38

796,925.72 132,820.95 1.40 80.41 1,288.50 3,076.36 0.0019 520.00 64,468,557.69

863,336.19 199,231.43 1.34 77.01 1,694.58 3,380.00 0.0013 780.00 42,979,038.46

929,746.67 265,641.91 1.28 73.40 2,001.84 3,488.27 0.0010 1,040.00 32,234,278.85

996,157.15 332,052.38 1.23 70.53 2,291.57 3,676.96 0.0008 1,300.00 25,787,423.08

- 3,623,220.53 - 235,503,331.37 - 106,566,215.98 - 364,440,446.75

- 3,556,810.05 - 231,186,760.43 - 166,718,202.74 - 295,655,318.12

- 3,490,399.58 - 226,870,189.49 - 183,891,151.03 - 269,849,227.95

- 3,423,989.10 - 222,553,618.55 - 190,319,339.70 - 254,787,897.40

- 3,357,578.62 - 218,237,047.61 - 192,449,624.53 - 244,024,470.69

26,143,650.00 26,143,650.00 26,143,650.00 26,143,650.00 26,143,650.00 - 266,287,051.42 - 266,287,051.42 - 266,287,051.42 - 266,287,051.42 - 266,287,051.42 232,137,779.57 326,618,831.36 326,618,831.36 72.88%

233,042,601.79 236,129,025.72 282,119,970.91 268,085,889.85 282,119,970.91 268,085,889.85 62.95% 59.82%

237,593,495.32 260,727,728.63 260,727,728.63 58.18%

238,115,116.43 255,883,135.97 255,883,135.97 57.10%

Figure 14: Screen Snapshot of Detailed Analysis for Insulated Pipe Stress Utilization Analysis (2,600 m Water Depth)

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

As shown in figure 15 below, it can be concluded that the insulated pipe will not fail during installation as the stress utilization for the various top tension ratios considered is less than 1 (i.e. 100%).

Figure 15: Plot of Stress Utilization versus Guess Estimates of Top Tension Ratio for Insulated Pipe (2,600 m Water Depth)

Furthermore, the insulated pipe system had a higher stress utilization than the bare pipe for the guess of top tension ratios considered. For instance, at a top tension ratio guess estimate of 1.1, the stress utilization for the bare pipe and insulated pipe was estimated to be 59.03% and 72.88% respectively. This difference in stress utilization for the case under study can be attributed to the buoyancy effect induced by the added insulation material which ultimately increased its submerged weight. Figure 16 below shows a side-by-side snapshot/comparison of the stress utilization curve for the bare pipe and insulated pipe system.

Figure 16: Snapshot of Stress Utilization Comparison for Bare Pipe and Insulated Pipe (2,600 m Water Depth)

The snapshot of stress utilization comparison for bare pipe and insulated pipe presented in figure 16 suggest that the submerged weight of a pipe system plays a critical role in the overall stress experienced by the pipe system. [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

5.3 Case 3: Pipe-In-Pipe The project specification and requirements for pipeline systems are becoming very intensive as O&G operators search for new reservoirs in harsher deepwater environment in excess of 1500 m water depths in order to replace the fast depleting hydrocarbon production from shallow reservoirs and consequently meet the constant increasing demand and consumption for oil and gas energy. In deepwater fields, subsea pipelines are often used to transport the hydrocarbon from subsea wells operated with an elevated temperature and pressure (HP/HT) to the subsea production manifold or production platform at the surface. To avoid the flow assurance problems created by wax and hydrate formation in the pipeline, the fluid temperature in the flowline must be frequently kept considerably within the desired temperature range to prevent the formation of hydrates and/or wax [17]. Thus, deepwater subsea developments must address the flow assurance associated with pipe system. Designing pipelines capable of meeting these flow assurance demands in harsher deepwater environments can be very challenging. However, over the years the oil and gas industry has developed the Pipe-inPipe (PIP) concept as one of the toolbox for overcoming these challenges due to its thermal efficiency. The Pipe-in-Pipe (PIP) design concept consists of two main pipes; an inner or carrier pipe which is the main conduit responsible for transporting the hydrocarbon which is in concentric or eccentric arrangement with an outer jacket pipe which serves as a housing accommodating the inner pipe. The inner pipe is usually covered with an insulating material to prevent heat loss. The outer jacket pipe serves to protect the carrier pipe and the insulation from thermal degradation and damage. This sort of arrangement is known as dry insulation because the insulation used in covering the inner pipe is not in contact with the seawater due to the dry environment provided by the annulus between the outer pipe and the inner pipe. In addition, centralizers are used to prevent the direct contact of the carrier pipe and jacket pipe. The carrier pipe and jacket pipe have structural connections through the bulkheads or spacers. In most cases, and depending on the project specification and environmental conditions, the outer jacket pipe can be coated in order to get protection against corrosion. Figure 17 below shows a typical configuration of a PIP system.

Figure 17: Typical Pipe-in-Pipe Design Arrangement

Table 4 below shows a detailed description of the major components in a PIP system. Table 4: Major Components of a PIP Systema

SN

1

Component

Carrier (Inner) Pipe

Description/Function (s) Main pressure containment in the system designed to transport the produced hydrocarbon. Thus it is designed against internal pressure, burst and internal corrosion and to meet flow assurance requirements. It is also the smallest diameter in the assembly typically between 6'' to 12'' in diameter.

a

Components may vary depending on project requirements. Electrical heating elements may be added to significantly enhance flow assurance properties. [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

2

Insulation Layer

3

Centralizer

4

Jacket (Outer) Pipe

5

Coating Layer

6

Bulkheads

7

Water Stops

This is the layer that lies in between the inner and outer pipe. It is usually made of materials with very low thermal conductivity to meet flow assurance requirements. The most common material used in the industry as an insulation layer for the PIP system is the InTerPipe (ITP) Izoflex™ with a heat transfer coefficient value of 0.5 W/m2 K. Other insulation materials are polyurethane foam (PUF), mineral wool, and microporous insulation. Depending on the project requirements and scale of preference, each has specific advantages in terms of insulation performance, operating temperature range, and relative cost. These are solid polymer rings clamped onto to the inner pipe that are located at distinct points along the systems in between the inner and outer pipe. They are regularly spaced in intervals between 2 m and 3 m and serve as protection to the insulation material during assembly, reeling, and laying operation. It can also increase local heat losses along the system by serving as a medium for head transfer by conduction from the inner pipe to the outer pipe. May not be needed depending on the nature of the insulation layer used. Insulation layers with high compressive strength such as ITP Izoflex™ eliminates the use of centralizers in PIP systems [18, 19]. The jacket (outer) pipe provides external cover, shield and housing to both the inner pipe and insulation layer. It interfaces with the harsh external environment and as such susceptible to failure induced by external pressure. Thus, design considerations for the carrier pipe focuses on material toughness for fracture and fatigue. Considerations also given for hydrostatic collapse. The coating layer is a thin layer of external corrosion protection applied to the outer surface of the jacket (outer) pipe. It serves to protect the jacket pipe from corrosion due to unfavourable chemical reactions in the environment of the seabed. The Fusion Bonded Epoxy (FBE) is an example of a coating material used for the external anti corrosion services. The FBE protective surface is homogeneous and offers an excellent resistance to chemical reaction [20]. The bulkhead is designed to connect the inner pipe to the outer pipe at each pipeline termination. Intermediate bulkheads at intervals of approximately 1 km may be required for reeled PIP to allow top tension to be transferred between the outer pipe and the inner pipe. During installation, the tensioner holds the outer pipe only, so the inner pipe tends to fall down by its dead weight and may result in buckling at the sagbend area near the seabed if no intermediate bulkheads exist. These are interlocking clamp ring like structures made of polymers that are designed to limit the pipeline length that will be damaged in the event that the annulus is flooded due to the outer pipe’s failure by external overpressure or puncture. Water stops are not design code requirement but they are recommended for deepwater projects where recovery of the flooded pipeline is challenging.

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

The structural behaviour of a PIP system is governed by the overall behaviour of the pipe system and the mechanism of load transfer between the inner and outer pipe. PIP systems can be classified into two categories in terms of their structural behaviour and method of load transfer between the inner pipe and the outer pipe [21]. These are; 1. Complaint Systems: In this system, the method of load transfer between the inner and outer pipe is seamless throughout the length of the pipeline. Thus, no relative displacement between the pipes occurs. 2. Non-Compliant Systems: This is contrary to the complaint system. Here, the method of load transfer between the inner and outer pipe occurs at discrete locations. So far most of the larger size PIP flowline are installed using J-lay method. During the pipe welding and lowering process, the vessel tensioner grabs the outer pipe with the inner pipe free-standing inside the outer pipe. Therefore a large top lay tension is applied to the outer pipe while the inner pipe is under a sizable compression due to its own weight. A bulkhead is welded to the both inner and outer pipes with a predetermined spacing. As the PIP is being lowered toward the sea floor, the large lay tension on the outer pipe is gradually released, and the outer pipe tends to go back to its original length. This results in a push to the inner pipe from the outer pipe and develops a locked-in compression in the inner pipe and a locked-in tension in the outer pipe. In the ultra-deep water PIP case, the locked-in loads and locked-in stresses could be critical if they are not well addressed [22]. PIP systems encounter significant limitations in going deeper, mainly because of their increasing weights which induce severe installation issues. Let us consider the PIP system shown in figure 18 below with geometric and physical properties highlighted in table 5.

Figure 18: Pipe-in-Pipe (PIP) System

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Table 5: Pipe Data for Pipe-in-Pipe Case Study (2,600 m Water Depth)

Pipe-in-Pipe Pipe Data Symbols Value Steel X65 σy 448,159,223.21 E 2.07E+11 ρs 7,850.00

Parameters Material Type Grade Yield Strength Young's Modulus Density of Steel

S.I Units NA NA Pa Pa kg/m3

Density of Insulation

ρin

250.00

kg/m3

Density of Coating Inner Pipe Outer Diameter Inner Pipe Wall Thickness Inner Pipe Inner Diameter

ρco Do tp Di

900.00 0.3239 0.0191 0.2857

kg/m3

Insulation Outer Diameter Insulation Thickness

Do ti

in

0.3559 0.0160

m m

Insulation Inner Diameter

Diin

0.3239

m

Outer Pipe Outer Diameter Outer Pipe Wall Thickness

cp

Do tcp

0.3980 0.0103

m m

Outer Pipe Inner Diameter Coating Thickness

Dicp tco

0.3774 0.0025

m m

Coating Outer Diameter

Do

co

0.4030

m

c0

0.3980

m

Coating Inner Diameter

Parameters Hydrodynamic Area

Di

Pipe Geometric Properties Symbols Value Ah 0.1276

m m m

S.I Units 2

Inner Pipe Internal Area

Ai

0.0641

m 2 m

Inner Pipe External Area

Ao

0.0824

m2

Internal Pipe Steel Area

As

0.0183

m2

Area of Insulation

Ain

0.0171

m2

Outer Pipe Internal Area

Ai

op

0.1119

m

Outer Pipe External Area

Aoop

0.1244

m

Outer Pipe Steel Area

As

op

0.0125

m2

Coating Area Pipe Submerged Weight

Aco Ws

0.0003 1,136.61

m2

2 2

N/m

Using the same environmental data and guess estimates of top tension requirement from the previous analysis carried out for bare and insulated pipe, the stress utilization analysis was performed for the PIP system. Figure 19 shows a screen snapshot of the results with more details on the excel commands used to execute the calculations presented in appendix IV. As can be seen from table 5 above, the PIP system pipe’s submerged weight was calculated by; 𝑤𝑠 = [(𝜌𝑠 × 𝐴𝑠 ) + (𝜌𝑖𝑛 × 𝐴𝑖𝑛 ) + (𝜌𝑠 × 𝐴𝑜𝑝 𝑠 ) + (𝜌𝑐𝑜 × 𝐴𝑐𝑜 ) − (𝜌𝑤 × 𝐴ℎ )]𝑔

(5.3)

During pipe lay for a PIP system, the holding tension, (To) is applied on the outer pipe and pretension (Ti) is applied on the inner pipe at the top end of the PIP flowline so that 𝑇𝑣 = 𝑇𝑜 + 𝑇𝑖 (5.4) [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

In general, To>Ti as the lay tension is applied through the outer pipe. On this note, the whole bending stress in the system is bearded by the outer pipe. However, the two pipes are under unequal axial stresses as the axial force will be shared between the two pipes. For this analysis, the load share is assumed to be rigid and compliant. This assumption is justified because it is assumed that mechanical load shares or bulkheads will be used during installation [22, p. 4]. Thus, using the values in table 5, the axial stress in the PIP system will be calculated as; 𝐹𝑎 𝜎𝑎 = (5.5) 𝐴𝑠 + 𝐴𝑆𝑜𝑝 𝐹𝑎 = 𝑇𝑣 − 𝑤𝑠 𝑑 − 1⁄4 𝑃ℎ 𝜋(𝐷𝑜 + 2𝑡𝑐𝑜 )2 (5.6) When the PIP flowline is lowered on the seabed, the pipe axial forces and strains are relieved gradually due to removal of pipe weight effect. The outer pipe which is at higher tension will tend to shrink more than the inner pipe and will cause lock-in compression on the inner pipe and lock-in tension on the outer pipe assuming the impact of soil/pipe friction is negligible. Based on these premises, the screen snapshot of the calculated result using excel is presented in figure 19 below.

Principal Stresses | von. Mises Stress | Stress Utilization Parameters

Referenced Equation

Guess Estimates of Top Tension Ratio 1.2 1.3 1.4

Symbols

S.I Units

Top Tension Tension @ TDP

Tv Th

Angle of Inflection

θ

Hor. Dist TDP Arc Length Curvature Bending Radius Bending Stress

4.6 4.9 4.8 4.8 4.11

Axial Force

x s c R σb Fa

N N Radians Degrees m m per m m Pa Pa

5.6

-

Axial Stress

σa

Pa

5.5

Longitudinal Stress

σl

Hydrostatic Pressure

Ph

Hoop Stress

σh σe

Upper Fibre: Pa Lower Fibre: Pa Pa Pa Upper Fibre: Pa Lower Fibre: Pa

4.14a 4.14b 4.16 4.15 14.17a 14.17b

- 98,566,038.98 - 88,982,093.78 - 79,398,148.58 - 69,814,203.37 - 60,230,258.17 59,868,576.41 - 9,764,786.08 - 26,586,610.11 - 30,205,549.53 - 34,442,835.10 - 257,000,654.36 - 168,199,401.47 - 132,209,687.04 - 109,422,857.22 - 86,017,681.25 26,143,650.00 26,143,650.00 26,143,650.00 26,143,650.00 26,143,650.00

S.U

Pa %

von Mises Equi. Stress Max von Mises Equi. Stress Stress Utilization

1.1 3,250,698.88 295,518.08 1.48 84.78 803.13 2,848.16 0.0038 260.00 158,434,615.38

4.1

4.18

3,039,254.29 -

3,546,216.96 591,036.16 1.40 80.41 1,288.50 3,076.36 0.0019 520.00 79,217,307.69 2,743,736.21 -

3,841,735.04 886,554.24 1.34 77.01 1,694.58 3,380.00 0.0013 780.00 52,811,538.46 2,448,218.13 -

4,137,253.12 1,182,072.32 1.28 73.40 2,001.84 3,488.27 0.0010 1,040.00 39,608,653.85 2,152,700.05 -

1.5 4,432,771.20 1,477,590.40 1.23 70.53 2,291.57 3,676.96 0.0008 1,300.00 25,787,423.08 1,857,181.97

- 505,105,470.87 - 505,105,470.87 - 505,105,470.87 - 505,105,470.87 - 505,105,470.87 537,546,024.66 500,294,554.12 492,350,832.56 490,700,441.83 488,795,029.80 437,456,782.45

445,493,139.66

537,546,024.66 500,294,554.12 119.95% 111.63%

453,686,127.00

460,255,162.46

492,350,832.56 109.86%

490,700,441.83 488,795,029.80 109.49% 109.07%

Figure 19: Screen Snapshot of Detailed Analysis for Pipe-in-Pipe Stress Utilization Analysis (2,600 m Water Depth)

Based on the results shown in figure 19 above and plotted curve shown in figure 20 below, it can be concluded that the PIP flowline will fail during installation by buckling as the stress utilization for the various top tension ratios considered is more than 1 (i.e. 100%). Thus, the top tension ratio has to be adjusted by increasing the tension at the tensioner in order to accommodate the submerged weight of the PIP. This off course will have some financial implication for the operator. Despite the benefits offered by PIP system, this is one of the penalty operators must face for installation to be successful. However, the cost-benefit ratio (CBR) is worth making the financial commitment to ensuring a successful pipeline installation operation. Alternatively, operators may consider optimizing the PIP design by minimizing the thickness of the components while still not compromising reliability. This may require the use of non API or DNV size for the flowline. This approach also advocates for additional cost and weight savings for deepwater operations. However, for shallow water applications, the benefit [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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468,062,577.87

Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

of this approach is limited and may not justify the additional design and/or procurement cost [23].

Figure 20: Plot of Stress Utilization versus Guess Estimates of Top Tension Ratio for Pipe-in-Pipe @ 2, 600 m Water Depth

6.0 Results and Discussion We have so far seen the impact of water depth, top tension ratio and pipe configuration on the stress utilization of pipe systems while laying using the S-Lay method from our analysis. As a discussion to the results of the analysis presented in the later sections, shown below is a comparison of the stress utilization for the various pipe configuration under study.

Figure 21: Stress Utilization Comparison for Bare Pipe and Pipe in Pipe (2,600 m Water Depth)

Figure 22: Stress Utilization Comparison for Insulated Pipe and Pipe in Pipe (2,600 m Water Depth)

Figures 21 and 22 above shows the comparison of the of stress utilization for PIP against bare pipe and insulted pipe. As can be seen, the PIP had a much higher stress utilization than the other pipes for the same operating conditions. This is as result of its much higher submerged weight than the submerged weight of other pipe configuration under study. It’s noteworthy to recall that this analysis was carried out by estimating the stress at the TDP which is the region in the system experiencing the most stress. Other part of the system along the submerged arch may experience a much lower amount of stress. More details on this will be discussed in the conclusion of this paper. Figure 23 on page 22 shows a comparison of the stress utilization for the three pipe configuration. [Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Figure 23: Stress Utilization Comparison for Bare Pipe, Insulated Pipe and Pipe in Pipe (2,600 m Water Depth)

7.0 Conclusion Table 6 below shows a summary of results for the stress utilization analysis at TDP carried out on the pipe systems under study. Table 6: Summary of Results for Stress Utilization @ TDP

Top Tension Ratio 1.1 1.2 1.3 1.4 1.5

SUMMARY OF RESULTS Stress Utilization @ 2,600 m Water Depth Bare Pipe Insulated Pipe Pipe in ipe 59.05% 72.88% 119.95% 53.75% 62.95% 111.63% 52.86% 59.82% 109.86% 52.63% 58.18% 109.49% 52.61% 57.10% 109.07%

As seen on table 6, the PIP system is over stressed at the touch down point (TDP) while the other pipe systems are under stressed. To further assess the pipe’s mechanical behaviour to stress along its submerged length, we can check for the stress utilization at any point along the submerged length of the pipe using the basic catenary equations. Let us take for instance, the coordinate mid-point along TDP from the stinger tip, 𝑥 = 𝑥𝑠 ⁄2. The corresponding Y coordinate will be calculated by this expression; 𝑇ℎ 𝑤𝑠 𝑦= [cosh ( 𝑥) − 1] (𝑒𝑞. 7.1) 𝑤𝑠 𝑇ℎ Where Th and ws have their usual meaning. On this note the axial force from equation 4.13 will be calculated as; 𝐹𝑎 = 𝑇𝑣 − 𝑤𝑠 (𝑑 − 𝑦) − 1⁄4 𝑃ℎ 𝜋(𝐷𝑜 + 2𝑡𝑖 )2 (𝑒𝑞. 7.2) and the hydrostatic pressure 𝑃ℎ from equation 4.16 for completeness, is restated below; 𝑃ℎ = 𝜌𝑤 𝑔(𝑑 − 𝑦)

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems Table 7: Stress Utilization @ Xs/2

Top Tension Ratio 1.1 1.2 1.3 1.4 1.5

SUMMARY OF RESULTS - Half Way To TDP Stress Utilization @ Xs/2 and 2,600 m Water Depth Xs/2 Y @ Xs/2 Bare Pipe Insulated Pipe Pipe in Pipe SU SU SU 401.57 376.87 53.68% 64.21% 107.74% 644.25 452.83 46.21% 52.27% 96.08% 253.63 507.26 44.05% 47.86% 92.23% 1,000.92 520.00 43.49% 45.97% 91.37% 1,145.79 538.48 43.15% 44.52% 90.25%

Table 7 above shows the summary result for the new x,y coordinate. As can be seen, the pipe is less utilized at this point. This leads to the conclusion that during lay operation, the stress utilization along the submerged length of the pipe increases as the TDP is approached. Please see appendix VI for a more detailed calculation on Microsoft Excel™. Figure 24 below shows a plot of stress utilization for the three pipe configuration under study versus guess estimates of top tension at Xs/2.

Figure 24: Stress Utilization Comparison for Bare Pipe, Insulated Pipe and Pipe in Pipe @ Xs/2 (2,600 m Water Depth)

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

8.0 References [1] P. Dominique and F. Ian, “J-Lay and Steep S-Lay: Complementary Tools for Ultradeep Water,” in Offshore Technology Conference, Houston, 2007. [2] W. Lin, Z. Xiangfeng, L. Wei, Y. Qianjin, H. Ning and Z. Lei, “Conceptual Analysis of Stinger for Ultra-deepwater S-lay,” in The International Society of Offshore and Polar Engineers (ISOPE), Beijing, 2009. [3] T. Stefanusse, “Pipeline Installation Methods (Lay Methods),” 31 January 2014. [Online]. Available: https://anakkelautan.wordpress.com/2014/01/31/pipeline-installation-methods-laymethods/. [Accessed 13 March 2015]. [4] B. Yong and B. Qiang, “Chapter 34: Installation Design,” in Subsea Pipelines and Risers, Oxford, Elsevier, 2005, p. 607. [5] H. J. Chul, “Limitation and Comparison of S-Lay and J-Lay Methods,” in International Offshore and Polar Engineering Conference, Singapore, 1993. [6] S. Springman and C. Herbert, “Deepwater Pipelaying Operations and Techniques Utiliizing JLay Methods,” in Offshore Technology Conference, Houston, 1994. [7] D. McDonald, D. SUllivan, H. Choi and J. Ray, “The Next Genaration of J-Lay System,” in SPE International Petroleum Conference and Exhibition, Villahermose, 1996. [8] M. Purvis, “Craft and Cable Ships for Operation Pluto,” Trans INA, vol. 88, 1946. [9] Y. Goren, D. Yenzer, C. Cushing and N. Friedland, “The Reel Pipelay Ship - A New Concept,” in Offshore Technology Conference, Dallas, 1975. [10] J. Richard, P. Nuno, B. Graeme, T. Gregory, M. John, S. Tanja and B. Joachim, “High Strenght Carbon Steel and CRA Lined Pipe for Reel-Lay Installation,” in Offshore Technology Conference, Houston, 2013. [11] W. Iain and W. Peter, Bundle Pipeline Systems and Shell FRAM Development, Aberdeen: Subsea 7, 2012. [12] C. Smith, “The Towed Pipeline Technique as a Means of Installing a Connected Structure,” in Society for Underwater Technology, Subsea International Conference, Netherlands, 1993. [13] J. Rahtz and C. Kevin, “Towed Production Systems for Economic Field Development,” in Offshore Technology Conference , Houston, 1992. [14] S. Wright, Pipeline Installation and Commissioning, Aberdeen: J.P Kenny, 2015. [15] M. Fernandez, “Tow Technique for Marine Pipeline Installation,” in Energy Technology Conference and Exhibition, Houston, 1981. [16] S. Gong, K. Chen, X. Dang and W. Jin, “Parametric Study on the Mechanical Behavior of Submarine Pipeline for Deepwater S-lay Operation,” in International Society of Offshore and Polar Engineers (ISOPE), Hawaii, 2011. [17] H. Gary, K. Nauru and C. Han, “Expansion Analysis of Subsea Pipe-in-Pipe Flowline,” in International Offshore and Polar Engineering Conference, Honolulu, 1997. [18] Subsea 7, High Performance Pipe-in-Pipe: Technology Product and Overview, Aberdeen: Subsea 7, 2014. [19] T. Gordon, (. Abdulmajid and M. Al-Sharif, “Innovations key reeled pipe-in-pipe flowline for gulf deepwater project,” in Offshore Technology Conference, Houston, 2001. [20] Tenaris, “External Anticorrosion,” Tenaris, [Online]. Available: http://www.tenaris.com/en/Products/OffshoreLinePipe/Coating/ExternalAnticorrosion.aspx. [Accessed 27 March 2015]. [21] B. Yong and B. Qiang, “Chapter 13: Pipe-in-Pipe and Bundle Systems,” in Subsea Pipelines and Risers, Oxford, Elvesier, 2005, pp. 198-199. [22] B. Ranil, S. Jason, J. Paul and C. Jack, “Analytical Estimation of Pretension Requirement to Inner Pipe of Pipe-in-Pipe Flowline in Ultra Deep Water Using J-Lay Installation,” in Offshore Technology Conference, Houston Texas, 2009. [23] M. Hausner and M. Dixon, “Optimized Design of Pipe-in-Pipe Systems,” in Offshore Technology Conference, Houston, 2002.

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

9.0 Appendices Appendix I: Expressing

𝑥

𝜎𝑏 ( 𝑠) = 2

𝐸𝐷 𝑓(𝑇̅ ,𝑙,𝑑)

Recall from equation 4.8; 𝑇ℎ 𝑅= @ 𝑇𝐷𝑃 𝑤𝑠 The top tension ratio, 𝑇̅ is expressed as; 𝑇𝑣 𝑇̅ = 𝑤𝑠 𝑑

(𝑒𝑞. 9.1)

Recall from equation 4.6; 𝑇ℎ 𝑥𝑠 = ∙ sinh−1(tan 𝜃) 𝑤𝑠 Also, from equation 4.3; 𝑇𝑣 𝑤𝑠 𝑙 tan 𝜃 = = 𝑇ℎ 𝑇ℎ From equation 4.11, the bending stress experienced by the pipe during lay operation is expressed as; 𝐷𝑜 𝜎𝑏 = ±𝐸 2𝑅 Substituting R into equation 4.11 yields; 𝑤𝑠 𝜎𝑏 = 𝐸𝐷𝑜 2𝑇ℎ Substituting 𝑇ℎ from equation 4.3 and 𝑤𝑠 from equation 9.1 into 9.2 yields; 𝑇𝑣 tan 𝜃 𝜎𝑏 = 𝐸𝐷𝑜 2𝑤𝑠 𝑙𝑇̅𝑑

(𝑒𝑞. 9.2)

(𝑒𝑞. 9.3)

From equation 4.6, 𝑤𝑠 can be expressed in terms of 𝑥𝑠 as; 𝑇ℎ 𝑤𝑠 = sinh−1 (tan 𝜃) 𝑥𝑠 Hence, equation 9.4 becomes; 𝑥𝑠 𝐸𝐷𝑜 tan 𝜃 𝑇𝑣 𝜎𝑏 = ( ) 2 𝑇̅𝑙𝑑 sinh−1 (tan 𝜃) 𝑇ℎ

(𝑒𝑞. 9.4)

Recall from equation 4.4; 𝑇𝑣 = tan 𝜃 𝑇ℎ Thus, equation 9.4 can be expressed as; 𝑥𝑠 𝐸𝐷𝑜 tan2 𝜃 𝜎𝑏 = ( ) 2 𝑇̅𝑙𝑑 sinh−1 (tan 𝜃)

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Appendix II: Detailed Excel Commands Used for Bare Pipe Stress Utilization Calculation Principal Stresses | von. Mises Stress | Stress Utilization

Parameters

Symbols

S.I Units

Referenced Equation

Guess Estimates of Top Tension Ratio

Bare Pipe

1.1 Top Tension Tension @ TDP

Tv Th

x s c R σb

N N Radians Degrees m m per m m Pa

4.6 4.9 4.8 4.8 4.11

Axial Force

Fa

Pa

4.12

Axial Stress

σa

4.13 4.14a

=Axial_Stress_1st_Guess+Bending_Stress_1st_Guess

Longitudinal Stress

σl

Pa Upper Fibre: Pa Lower Fibre: Pa Pa Pa Upper Fibre: Pa Lower Fibre: Pa

=Pipe_Submerged_Weight*Water_Depth*Top_Tension_Ratio_1st_Guess =Top_Tension_1st_Guess-(Water_Depth*Pipe_Submerged_Weight) =ACOS(Tension_at_TDP_1st_Guess/Top_Tension_1st_Guess) =ACOS(Tension_at_TDP_1st_Guess/Top_Tension_1st_Guess)*(180/PI()) =(Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight)*ASINH(TAN(Angle_of_Inflection_1st_Guess)) =(Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight)*TAN(Angle_of_Inflection_1st_Guess) =Pipe_Submerged_Weight/Tension_at_TDP_1st_Guess =Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight =(Pipe_Outer_Diameter*Young_s_Modulus)/(2*Bending_Radius_1st_Guess) =(Top_Tension_1st_Guess-(Pipe_Submerged_Weight*Water_Depth)(Density_of_Seawater*Acc._due_to_Gravity*Water_Depth*PI()*Pipe_Outer_Diameter^2*0.25)) =Axial_Force_1st_Guess/Area_of_Steel

Angle of Inflection

θ

Hor. Dist TDP Arc Length Curvature Bending Radius Bending Stress

4.14b

=Axial_Stress_1st_Guess-Bending_Stress_1st_Guess

4.16 4.15

=Density_of_Seawater*Acc._due_to_Gravity*Water_Depth =-(Hydrostatic_Pressure_1st_Guess*Pipe_Outer_Diameter)/(2*Pipe_Wall_Thickness)

Hydrostatic Pressure Hoop Stress

Ph σh

von Mises Equi. Stress σe Max von Mises Equi. Stress Stress Utilization

Pa S.U

%

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

4.1

14.17a

=SQRT((Long_Stress_UFiber_1st_Guess^2)+(Hoop_Stress_1st_Guess^2)-(Long_Stress_UFiber_1st_Guess*Hoop_Stress_1st_Guess))

14.17b

=SQRT((Long_Stress_LFiber_1st_Guess^2)+(Hoop_Stress_1st_Guess^2)-(Long_Stress_LFiber_1st_Guess*Hoop_Stress_1st_Guess))

4.18

=MAX(Equ_Stress_UFiber_1st_Guess,Equ_Stress_LFiber_1st_Guess) =Max_von_Mises_Equi._Stress_1st_Guess/Yield_Strength

Page 26

Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Appendix III: Detailed Excel Commands Used for Insulated Pipe Stress Utilization Calculation Principal Stresses | von. Mises Stress | Stress Utilization

Parameters

Symbols

S.I Units

Referenced Equation

Guess Estimates of Top Tension Ratio

Insulated Pipe

1.1 Top Tension Tension @ TDP

Tv Th

x s c R σb

N N Radians Degrees m m per m m Pa

4.6 4.9 4.8 4.8 4.11

Axial Force

Fa

Pa

4.12

Axial Stress

σa

4.13 4.14a

=Axial_Stress_1st_Guess+Bending_Stress_1st_Guess

Longitudinal Stress

σl

Pa Upper Fibre: Pa Lower Fibre: Pa Pa Pa Upper Fibre: Pa Lower Fibre: Pa

=Pipe_Submerged_Weight*Water_Depth*Top_Tension_Ratio_1st_Guess =Top_Tension_1st_Guess-(Water_Depth*Pipe_Submerged_Weight) =ACOS(Tension_at_TDP_1st_Guess/Top_Tension_1st_Guess) =ACOS(Tension_at_TDP_1st_Guess/Top_Tension_1st_Guess)*(180/PI()) =(Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight)*ASINH(TAN(Angle_of_Inflection_1st_Guess)) =(Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight)*TAN(Angle_of_Inflection_1st_Guess) =Pipe_Submerged_Weight/Tension_at_TDP_1st_Guess =Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight =(Pipe_Outer_Diameter*Young_s_Modulus)/(2*Bending_Radius_1st_Guess) =(Top_Tension_1st_Guess-(Pipe_Submerged_Weight*Water_Depth)(Density_of_Seawater*Acc._due_to_Gravity*Water_Depth*PI()*(Pipe_Outer_Diameter+2*Insulation_Thickness)^2*0.25)) =Axial_Force_1st_Guess/Area_of_Steel

Angle of Inflection

θ

Hor. Dist TDP Arc Length Curvature Bending Radius Bending Stress

4.14b

=Axial_Stress_1st_Guess-Bending_Stress_1st_Guess

4.16 4.15

=Density_of_Seawater*Acc._due_to_Gravity*Water_Depth =-(Hydrostatic_Pressure_1st_Guess*Pipe_Outer_Diameter)/(2*Pipe_Wall_Thickness)

Hydrostatic Pressure Hoop Stress

Ph σh

von Mises Equi. Stress σe Max von Mises Equi. Stress Stress Utilization

Pa S.U

%

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

4.1

14.17a

=SQRT((Long_Stress_UFiber_1st_Guess^2)+(Hoop_Stress_1st_Guess^2)-(Long_Stress_UFiber_1st_Guess*Hoop_Stress_1st_Guess))

14.17b

=SQRT((Long_Stress_LFiber_1st_Guess^2)+(Hoop_Stress_1st_Guess^2)-(Long_Stress_LFiber_1st_Guess*Hoop_Stress_1st_Guess))

4.18

=MAX(Equ_Stress_UFiber_1st_Guess,Equ_Stress_LFiber_1st_Guess) =Max_von_Mises_Equi._Stress_1st_Guess/Yield_Strength

Page 27

Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Appendix IV: Detailed Excel Commands Used for Pipe in Pipe Stress Utilization Calculation Principal Stresses | von. Mises Stress | Stress Utilization

Pipe in Pipe

Parameters

Symbols

Top Tension Tension @ TDP

Tv Th

Angle of Inflection

θ

Hor. Dist TDP Arc Length Curvature Bending Radius Bending Stress

S.I Units

Referenced Equation

x s c R σb

N N Radians Degrees m m per m m Pa

4.6 4.9 4.8 4.8 4.11

Axial Force

Fa

Pa

5.6

Axial Stress

σa

Pa Upper Fibre: Pa Lower Fibre: Pa Pa Pa Upper Fibre: Pa Lower Fibre: Pa

5.5

Longitudinal Stress Hydrostatic Pressure Hoop Stress

σl Ph σh

von Mises Equi. Stress σe Max von Mises Equi. Stress Stress Utilization

Pa S.U

%

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

4.1

Guess Estimates of Top Tension Ratio 1.1 =Pipe_Submerged_Weight*Water_Depth*Top_Tension_Ratio_1st_Guess =Top_Tension_1st_Guess-(Water_Depth*Pipe_Submerged_Weight) =ACOS(Tension_at_TDP_1st_Guess/Top_Tension_1st_Guess) =ACOS(Tension_at_TDP_1st_Guess/Top_Tension_1st_Guess)*(180/PI()) =(Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight)*ASINH(TAN(Angle_of_Inflection_1st_Guess)) =(Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight)*TAN(Angle_of_Inflection_1st_Guess) =Pipe_Submerged_Weight/Tension_at_TDP_1st_Guess =Tension_at_TDP_1st_Guess/Pipe_Submerged_Weight =(Outer_Pipe_Outside_Diameter*Young_s_Modulus)/(2*Bending_Radius_1st_Guess) =(Top_Tension_1st_Guess-(Pipe_Submerged_Weight*Water_Depth)(Density_of_Seawater*Acc._due_to_Gravity*Water_Depth*PI()*(Outer_Pipe_Outside_Diameter+2*Coating_Thickness)^2*0.25)) =Axial_Force_1st_Guess/(Internal_Pipe_Steel_Area+Outer_Pipe_Steel_Area)

4.14a

=Axial_Stress_1st_Guess+Bending_Stress_1st_Guess

4.14b

=Axial_Stress_1st_Guess-Bending_Stress_1st_Guess

4.16 4.15

=Density_of_Seawater*Acc._due_to_Gravity*Water_Depth =-(Hydrostatic_Pressure_1st_Guess*Outer_Pipe_Outside_Diameter)/(2*Outer_Pipe_Wall_Thickness)

14.17a

=SQRT((Long_Stress_UFiber_1st_Guess^2)+(Hoop_Stress_1st_Guess^2)-(Long_Stress_UFiber_1st_Guess*Hoop_Stress_1st_Guess))

14.17b

=SQRT((Long_Stress_LFiber_1st_Guess^2)+(Hoop_Stress_1st_Guess^2)-(Long_Stress_LFiber_1st_Guess*Hoop_Stress_1st_Guess))

4.18

=MAX(Equ_Stress_UFiber_1st_Guess,Equ_Stress_LFiber_1st_Guess) =Max_von_Mises_Equi._Stress_1st_Guess/Yield_Strength

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Effects of Top Tension on Stress Utilization in Pipe Laying Operations: A Case Study for Bare Pipe, Insulated Pipe and Pipe-In-Pipe Systems

Appendix V: Given Data for Assignment

Appendix VI – Excel Spread Sheet Showing Detailed Calculations and Formulas S/N

1

DESCRIPTION The attached spread sheet workbooks contains three sheets for the cases of pipe configuration. The sheets are titled;  Bare Pipe: Contains Stress Utilization Calculation for the bare pipe system and a plot of stress utilization versus water depth.  Insulated Pipe: Contains Stress Utilization Calculation for the insulated pipe system, a plot of stress utilization versus water depth for the insulated pipe system and a comparison of the stress utilization for the bare pipe and insulated pipe versus water depth.  Pipe in Pipe: Contains Stress Utilization Calculation for the PIP pipe system, a plot of stress utilization versus water depth for the PIP pipe system and a comparison of the stress utilization for the bare pipe, insulated pipe, and PIP pipe system versus water depth.

FILE

COMMENTS

SU Calculation @TDP.xlsx

Please Double Click to Open Embedded Document.

SU Calculation @Half Xs.xlsx

[Prepared by Chima Clement | 51444886 | EG55F1 | March 2015]

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