caused by low pressure shut-down in the annulus) but also for crushing loads during installation operations, handling of the pipe, and pippin tools.
Issues about internal pressure, which may cause high hoop stresses, can be avoided or limited designing a pressure armor. It is a corrugate profile which shows notable strength in the hoop direction, where the cross-sections are interlocked and free to slide one to each other, in order to confer low bending stiffness at the same time. The metallic cross-section can have different forms; the most used Z-shaped and C-shaped are illustrate in Figure 1.5.
When dealing with deep waters, withstanding high tension is one of the main challenges. Strips are too thin to carry substantial axial loads and they must be increased in size, for rectangular or close to rectangular shape. Thus, a proper design provides the employment of wires, in two or four layers winded at an angle with the longitudinal axis within about 35° and 55°. The winding angle is opposite one by one, or two by two, layers to provide torsional resistance for the two directions.
Figure 1.5 Pressure armor cross-section profiles.
1.6 Project and Objectives
This part aims to understand the need of supplementary elements such us interlocked carcass and tensile armor wires to support the design in case of extreme environmental conditions. To satisfy safe and proficient operation of flexible pipelines in deep water conditions, numerical and theoretical models are developed, which must lead to an accurate prediction of the strength with respect to the critical failure modes. Comparisons among results are made and enhanced cross-sectional profiles are carried out for the case of metallic strip flexible pipe and MSFP.
In order to do so, the base cases have been deeply studied, and already existing both theoretical and numerical models applied. According to API recommended practice 17B, innovative cross-sections for both cases are established, combining different hypothesis and theories and verifying results with the commercial finite element software ABAQUS, which hopefully provide both useful information and understanding.
Critical conditions for two different load cases are studied, such external pressure and tensile load, which as previously said, and are strictly connected for deep water conditions. Against high external pressure, the interlocked carcass is essential in order to prevent collapse. Being of intricate shape, theoretical models which turn into equivalent reproductions are used. In this work, wide spectrum of FEM for different geometries is analyzed and an empirical formulation is carried out for the minimum requirement of ovality, which suggests a modified theoretical model closer to the more realistic behavior of the numerical simulation.
Strength against wide tensile loads is provided by the tensile armor layers. A profile also including pressure armor is considered; again, an equivalent theoretical model is employed to catch its particular behavior due to its shape. A simplified theoretical model is obtained which is confirmed by a numerical simulation. The validated model is then extended to understand the performance when the pipe is subjected to combined tensile force and external pressure.
References
1. N. Ismail, R. Nielsen, and M. Kanarellis, Design Considerations for Selection of Flexible Riser Configuration, PD-Vol. 42, Offshore and Arctic Operations, ASME, 1992.
2. Ruan W, Bai Y, Cheng P. Static analysis of deepwater lazy-wave umbilical on elastic seabed[J]. Ocean Engineering, 2014, 91: 73–83.
3. Garrett D L. Dynamic analysis of slender rods[J]. J. Energy Resour. Technol.;(United States), 1982, 104(4).
4. Croll J G A. Bending boundary layers in tensioned cables and rods[J]. Applied ocean research, 2000, 22(4): 241–253.
5. Bai Y, and Bai Q. Subsea pipelines and risers. Elsevier, 2005.
6. Palmer A C, King R A. Submarine Pipeline Engineering[M]. PennWell Books, 2004.
7. Orcina Ltd., Visual ORCAFLEX User Manual, Ulverston, Cumbria, UK, 2000.
2
Structural Design of Flexible Pipes in Different Water Depth
2.1 Introduction
Flexible pipelines must be designed considering the extreme case in which a leakage through the layers can happen. The external pressure would be applied directly on the innermost PE layer, which provides only hydraulic insulation thus to the carcass surface. Mostly, the issue is relevant for deep water depth because of high hydrostatic pressures and tools to design the interlocked carcass under code requirements are needed. This work aims to give an estimation of the critical buckling load for interlocked carcass accounting for imperfections, which is valid when the profile can be considered as thin wall. The collapse behavior is influenced by the initial geometrical imperfections which can be depicted solving the problem on an ovalized deformed shape. The numerical simulation aims to reproduce the actual behavior of the structure, validating the theoretical model. The analyzed case has been also compared with two corresponding steel strips reinforced thermoplastic pipes (SSRTP), in order to evaluate when the support of the interlocked carcass is needed for a real design and environmental conditions case. The results obtained from the theoretical and the numerical simulations lead to a remarkable confidence in the models thanks to a relatively small difference achieved between the outcomes. This chapter is quoted from Ref. [1].
2.2 Theoretical Models
The well-known differential equation by Timoshenko et al. [2] for the helical shape of a thin bar is used in this work. The following approach considers the bending moment on a steel ring having an original imperfection. Here, the tangential displacements can be neglected being interested in the radial problem:
where radial displacements uR are considered to be small, is the circumferential reference of the helical element, M is the bending moment acting on each cross section, E is the modulus of Young of the material, and I and R are the moment of inertia of the cross-section and the internal radius of the ring respectively, as can be seen in Figure 2.1.
The assumption of initial imperfection leads to an extension of Eq. (2.1), considering that, under this hypothesis, the bending moment in each cross section can be computed as
for which, uR1 is the initial radial displacement, and p is the uniform pressure applied on the external surface of the bar. The initial displacement is function of the circumferential reference coordinate (R) and also of the initial ovality1 so that
