A Nonlinear Analysis Formulation for Bend Stiffeners

2007 ◽  
Vol 51 (03) ◽  
pp. 250-258 ◽  
Author(s):  
M. A. Vaz ◽  
C. A. D. de Lemos ◽  
M. Caire
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Nonlinear Analysis ◽  
Cross Section ◽  
Contact Force ◽  
Oil And Gas ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Power Series Expansion ◽  
Gas Production

Bend stiffeners are polymeric structures with a conical shape designed to limit the curvature of flexible risers and umbilical cables at their uppermost connections, protecting them against overbending and from accumulation of fatigue damage. Thus, they are of vital importance to deep water oil and gas production systems. This work develops a mathematical formulation and a numerical solution procedure for the geometrical and material nonlinear analysis of the riser/bend stiffener system considered as a beam bending model. The structures are separately modeled, which allows the numerical calculation of the contact force along the system arc length. The governing differential equations are derived considering geometrical compatibility, equilibrium of forces and moments, and nonlinear asymmetric material constitutive relations, which leads to a shift in the neutral axis position from the cross-section centroid. The eccentricity and the bending moment versus curvature relation for each cross section are numerically calculated and then expressed by a polynomial power series expansion. A set of four first-order nonlinear ordinary differential equations is written and four boundary conditions are specified at both ends. Once the global problem is solved, the contact force may be promptly calculated. A finite difference method is implemented in Fortran code to obtain the numerical solution. A case study is carried out where linear elastic symmetric and nonlinear elastic asymmetric constitutive models are compared and discussed. The results are presented for the riser/bend stiffener deflected configuration, angle, curvature, and contact force distribution. The results demonstrate that an accurate structural analysis of bend stiffeners depends on a precise assessment of the nonlinear asymmetric polyurethane property.

Geometrical and Material Non-Linear Formulation for Bend Stiffeners

2004 ◽  
Author(s):  
Murilo Augusto Vaz ◽  
Carlos Alberto Duarte de Lemos
Keyword(s):  
Differential Equations ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Power Series Expansion ◽  
Constitutive Models ◽  
Bending Moment ◽  
Accurate Analysis ◽  
Linear Ordinary Differential Equations ◽  
Linear Elastic ◽  
Non Linear

A mathematical formulation and a numerical solution for the geometrical and material non-linear analysis of bend stiffeners — employed to protect the upper terminations of flexible risers and subsea umbilical cables — are presented in this paper. The differential equations governing the problem result from geometrical compatibility, equilibrium of forces and moments and material constitutive relations, which can be linear elastic symmetric or non-linear elastic asymmetric. In this latter case, the bending moment versus curvature for each cross-section is calculated and then expressed by a polynomial power series expansion. Hence, a set of four first order non-linear ordinary differential equations is written and boundary conditions are defined at both ends. A one-parameter shooting method is employed and results are presented for a case study where linear elastic symmetric and non-linear elastic asymmetric constitutive models are compared and discussed. It is shown that an accurate analysis of bend stiffeners depends on a precise assessment of the material constitutive property.

An Analysis of the Motion of Pigs Through Gas Pipelines

1984 ◽  
Vol 106 (4) ◽  
pp. 374-379 ◽  
Author(s):  
J. S. Weingarten ◽  
A. J. Chapman ◽  
W. F. Walker
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Numerical Solution ◽  
Cross Section ◽  
Nonlinear Differential Equations ◽  
Gas Pipeline ◽  
Gas Pipelines ◽  
Governing Equations ◽  
One Dimensional ◽  
Solution Scheme

A one-dimensional, quasi-steady, model describing the motion of a pig moving in a gas pipeline is developed for the cases of a solid pig, which obstructs the cross section of the pipe, and one with a concentric hole through it. The resultant governing equations constitute a set of seven nonlinear differential equations. A numerical solution scheme, implemented by a computer program, is described. Results and discussion are presented for a set of typical cases.

Viscoelastic Analysis of Bend Stiffeners

2005 ◽  
Author(s):  
Marcelo Caire ◽  
Murilo Augusto Vaz ◽  
Carlos Alberto Duarte de Lemos
Keyword(s):  
Numerical Solution ◽  
Mechanical Response ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Viscoelastic Behaviour ◽  
Elastic Behaviour ◽  
Creep Function ◽  
Creep Tests ◽  
Accurate Analysis ◽  
Linear Viscoelastic

Bend stiffeners are polymeric structures employed to ensure a smooth and safe transition in the upper connection of risers and umbilical cables, protecting them against accumulation of fatigue damage and excessive curvatures. Recent failures have stimulated a better understanding of the mechanical response in order to increase the reliability in design and analysis of bend stiffeners. This work presents a mathematical formulation that represents the system riser/bend stiffener considering geometric non linearity and polyurethane with viscoelastic behaviour, an inherent characteristic to polymers. The following assumptions are considered: cross-sections remain plane after deformation, large deflections are accepted but it is a small strain bending problem, the self-weight and external forces are disregarded and the material is assumed with linear viscoelastic behaviour. The curves that represent the viscoelastic response of the material have been raised by means of creep tests, whose specimens were cut from actual bend stiffeners. The time dependent data obtained in the experimental tests were well approximated by a third order Prony series which describes the creep function. The set of four first order non linear ordinary differential equations results from geometrical compatibility, equilibrium of forces and moments and linear viscoelastic constitutive relations. The numerical solution of the problem is obtained using a one-parameter shooting method. The results are then compared with the consolidated numerical solution for linear elastic material. It is concluded that the viscoelastic phenomena can lead to excessive curvatures on the upper terminations of risers and umbilical cables if the polymeric structure were designed considering elastic behaviour. The correct characterization of the viscoelastic properties of polyurethane used on bend stiffeners must be taken into account when accurate analysis is desired.

Backscattering Analysis of Cylinder Shaped Scatterer in Vegetation Medium: Comparison Between Theories

2020 ◽  
Vol 2 (1) ◽  
pp. 15-18
Author(s):  
Syabeela Syahali ◽  
Ewe Hong Tat ◽  
Gobi Vetharatnam ◽  
Li-Jun Jiang ◽  
Hamsalekha A Kumaresan
Keyword(s):  
Numerical Solution ◽  
Cross Section ◽  
Traditional Method ◽  
Microwave Remote Sensing ◽  
Solution Model ◽  
Complex Nature ◽  
Good Match ◽  
Equivalent Source ◽  
Backscattering Cross Section ◽  
Method Model

This paper analyses the backscattering cross section of a cylinder both using traditional method model and a new numerical solution model, namely Relaxed Hierarchical Equivalent Source Algorithm (RHESA). The purpose of this study is to investigate the prospect of incorporating numerical solution model into volume scattering calculation, to be applied into microwave remote sensing in vegetation area. Results show a good match, suggesting that RHESA may be suitable to be used to model the more complex nature of vegetation medium.

METHANE DETECTION FOR OIL AND GAS PRODUCTION SITES USING PORTABLE DUAL-COMB SPECTROMETRY

2016 ◽  
Author(s):  
Sean Coburn ◽  
Greg Rieker ◽  
Kuldeep Prasad ◽  
Subhomoy Ghosh ◽  
Caroline Alden ◽  
...  
Keyword(s):  
Oil And Gas ◽  
Gas Production ◽  
Oil And Gas Production ◽  
Methane Detection
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