Fatigue Life Prediction Due to Slug Flow in Extra Long Submarine Gas Pipelines Using Fourier Expansion Series

2009 ◽  
Author(s):  
Euro Casanova ◽  
Orlando Pelliccioni ◽  
Armando Blanco
Keyword(s):  
Fatigue Life ◽  
Dynamic Response ◽  
Slug Flow ◽  
Fourier Expansion ◽  
Time Integration ◽  
Computational Cost ◽  
Gas Production ◽  
Computational Time ◽  
Integration Scheme ◽  
Expansion Series

Some offshore gas production fields require transporting of production fluids through very long submarines pipelines, without a previous separation process. In these cases, a slug flow pattern may develop for some production conditions. Condensate slugs traveling in the pipeline, act as moving loads for the piping structure, especially for the unsupported pipe spans which can be of even hundreds of meters long, due to irregular sea bottom, therefore producing a dynamic response of the pipeline that in some cases may significantly reduce its fatigue life. In this work a previously presented model [1], which combines fluid equations for predicting slug characteristics and a structural finite element model of horizontal pipelines transporting slugs, is modified for reducing computational cost and to adapt fatigue life calculations to the case of submarine piping. In order to calculate maximum amplitudes of the dynamic response without a time integration scheme, it is considered that traveling slugs produce periodical loads in time for every spatial point of the pipeline, and consequently these loads may be expressed by means of Fourier expansion series. With these assumptions, a more realistic fatigue calculation for a diversity of pipelines conditions is obtained. Results show that for this improved model computational time is dramatically reduced, without a lost in precision, when compared to the previous model requiring a time integration process.

Fatigue Life Prediction Due to Slug Flow in Extra Long Submarine Gas Pipelines

2008 ◽  
Author(s):  
Rabih Kansao ◽  
Euro Casanova ◽  
Armando Blanco ◽  
Frank Kenyery ◽  
Mayela Rivero
Keyword(s):  
Fatigue Life ◽  
Dynamic Response ◽  
Slug Flow ◽  
Gas Production ◽  
Hydrodynamic Characteristics ◽  
Fe Model ◽  
Moving Loads ◽  
Gas Field ◽  
Steady State Condition ◽  
Production Conditions

Some offshore production fields require transporting of production fluids through very long submarines pipelines without a previous separation process. In the case of gas production, condensate will appear in the pipeline due to the pressure losses and low temperatures. For some production conditions a slug flow pattern may then develop in the pipeline, and because of the irregular sea bottom profile, there may be pipe unsupported spans of even hundreds of meters long. Therefore, slugs traveling in the pipeline will act as moving loads for the unsupported pipe, producing a dynamic response that in some cases might reduce the fatigue life of the pipeline. In this work, a finite element (FE) model of a pipeline transporting slugs has been developed and used to assess the fatigue life of a horizontal pipeline. Slug hydrodynamic characteristics have been obtained using Taitel & Barnea’s model. The structural FE model is based in Bernoulli beam elements where slugs, once they have been geometrically characterized, are input as moving loads traveling in the pipeline. The system dynamic response was calculated for different spans conditions and slugs characteristics corresponding to different gas-liquid ratios typical from gas field production conditions. Once a steady state condition was obtained in the dynamic response, mean and alternating stress levels were obtained for each analyzed case and introduced in fatigue formulae to obtain the fatigue life of the pipeline. Results show that for some production conditions and free span longitudes, fatigue life of pipeline may experience important reductions due to slug flow. These free spans are obviously most likely to happen in extra long submarines pipelines.

A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Akbar Gholampour ◽  
Mehdi Ghassemieh ◽  
Mahdi Karimi-Rad
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Numerical Dispersion ◽  
Computational Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Similar Time ◽  
Unconditionally Stable ◽  
Average Acceleration

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

scholarly journals Lagrangian meshfree finite difference particle method with variable smoothing length for solving wave equations

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878924 ◽  
Author(s):  
Sheng Wang ◽  
Yong Ou Zhang ◽  
Jing Ping Wu
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Time Integration ◽  
Simple Wave ◽  
Domain Size ◽  
Particle Method ◽  
Computational Time ◽  
Integration Scheme ◽  
Smoothed Particle ◽  
Support Domain

In a Lagrangian meshfree particle-based method, the smoothing length determines the size of the support domain for each particle. Since the particle distribution is irregular and uneven in most cases, a fixed smoothing length sometime brings too much or insufficient neighbor particles for the weight function which reduces the numerical accuracy. In this work, a Lagrangian meshfree finite difference particle method with variable smoothing length is proposed for solving different wave equations. This pure Lagrangian method combines the generalized finite difference scheme for spatial resolution and the time integration scheme for time resolution. The new method is tested via the simple wave equation and the Burgers’ equation in Lagrangian form. These wave equations are widely used in analyzing acoustic and hydrodynamic waves. In addition, comparison with a modified smoothed particle hydrodynamics method named the corrective smoothed particle method is also presented. Numerical experiments show that two kinds of Lagrangian wave equations can be solved well. The variable smoothing length updates the support domain size appropriately and allows the finite difference particle method results to be more accurate than the constant smoothing length. To obtain the same level of accuracy, the corrective smoothed particle method needs more particles in the computation which requires more computational time than the finite difference particle method.

scholarly journals Explicit meshfree $${{\varvec{u}}}-{{\varvec{p}}}_\mathbf{\mathrm{w}}$$ solution of the dynamic Biot formulation at large strain

2021 ◽  
Author(s):  
Pedro Navas ◽  
Miguel Molinos ◽  
Miguel M. Stickle ◽  
Diego Manzanal ◽  
Angel Yagüe ◽  
...  
Keyword(s):  
Pore Water Pressure ◽  
Large Strain ◽  
Water Pressure ◽  
Time Integration ◽  
Computational Cost ◽  
Local Maximum ◽  
Integration Scheme ◽  
Time Integration Scheme ◽  
Biot’S Equations ◽  
Predictor Corrector

AbstractIn this paper, an efficient and robust methodology to simulate saturated soils subjected to low-medium frequency dynamic loadings under large deformation regime is presented. The coupling between solid and fluid phases is solved through the dynamic reduced formulation $$u-p_\mathrm{w}$$ u - p w (solid displacement – pore water pressure) of the Biot’s equations. The additional novelty lies in the employment of an explicit two-steps Newmark predictor-corrector time integration scheme that enables accurate solutions of related geomechanical problems at large strain without the usually high computational cost associated with the implicit counterparts. Shape functions based on the elegant Local Maximum Entropy approach, through the Optimal Transportation Meshfree framework, are considered to solve numerically different dynamic problems in fluid saturated porous media.

A Newly Developed Algorithm for Treating the Coupled Dynamic Response of Robotic Fixtureless Assembly

1996 ◽  
Author(s):  
Genady Shagal ◽  
Shaker A. Meguid
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Time Integration ◽  
Integration Scheme ◽  
The Finite Element Method ◽  
Coupled Equations ◽  
Time Integration Scheme ◽  
Implicit Approach ◽  
Cooperating Robots

Abstract The coupled dynamic response of two cooperating robots handling two flexible payloads for the purpose of fixtureless assembly and manufacturing is treated using a new algorithm. In this algorithm, the equations describing the dynamics of the system are obtained using Lagrange’s method for the rigid robot links and the finite element method for the flexible payloads. A new time integration scheme is developed to treat the coupled equations of motion of the rigid links for a given displacement of the flexible payloads. The finite element equations of the flexible payloads are then treated using an implicit approach. The new algorithm was verified using simplified examples and was later used to examine the dynamic response of two cooperating robot arms manipulating flexible payloads which are typical of the automotive industry.

A COMPOSITE TIME INTEGRATION SCHEME FOR DYNAMIC ADHESION AND ITS APPLICATION TO GECKO SPATULA PEELING

2014 ◽  
Vol 11 (05) ◽  
pp. 1350104 ◽  
Author(s):  
SACHIN S. GAUTAM ◽  
ROGER A. SAUER
Keyword(s):  
Nonlinear Response ◽  
Time Integration ◽  
Computational Cost ◽  
Integration Scheme ◽  
Time Step ◽  
Integration Schemes ◽  
Newmark Scheme ◽  
Highly Nonlinear ◽  
Time Integration Schemes ◽  
Time Integration Scheme

Simulation of dynamic adhesive peeling problems at small scales has attracted little attention so far. These problems are characterized by a highly nonlinear response. Accurate and stable time integration schemes are required for simulation of dynamic peeling problems. In the present work, a composite time integration scheme is proposed for the simulation of dynamic adhesive peeling problems. It is shown through numerical examples that the proposed scheme remains stable and also has some gain in accuracy. The performance of the scheme is compared with two collocation-based schemes, i.e., Newmark scheme and Bathe composite scheme. It is shown that the proposed scheme and Bathe composite scheme perform equally. However, the proposed scheme adds very little to the computational cost of Newmark scheme. Through a numerical simulation of the peeling of a gecko spatula from a rigid substrate it is shown that the proposed scheme and the Bathe composite scheme are able to simulate the complete peeling process for given time step whereas the Newmark scheme diverges. It is also shown that the maximum pull-off force is within the range reported in the literature.

INFLUENCE OF OBJECTIVE FUNCTIONS IN STRUCTURAL DAMAGE IDENTIFICATION USING REFINED AND SIMPLE MODELS

2009 ◽  
Vol 09 (04) ◽  
pp. 607-625 ◽  
Author(s):  
RICARDO PERERA ◽  
SHENG-EN FANG
Keyword(s):  
Dynamic Response ◽  
Objective Function ◽  
Structural Damage ◽  
Damage Identification ◽  
Computational Cost ◽  
Computational Time ◽  
Fe Model ◽  
Beam Model ◽  
Objective Functions ◽  
Multi Objective

The most usual approach for solving damage identification problems is the use of the finite element (FE) model updating method. To apply the method, a minimization of an objective function measuring the fit between measured and model predicted data is performed. Then, the success of the procedure depends strongly on the accuracy of the FE model and the choice of a suitable objective function. Although detailed FE models provide an accurate means for calculating the dynamic response of the structure, their size and complexity involve a large number of parameters to be updated and a high computational cost. In order to shorten the computational time, more simplified and practical models able to model the global dynamic response of the structure accurately would be desirable. Furthermore, working with several objective functions instead of only one would increase the robustness and performance of the procedure. In this paper, a multi-objective simple beam model is proposed and compared with a more refined model based on plane elements. Furthermore, in the multi-objective framework, different combinations of objective functions are studied. The reliability and effectiveness of the proposed model has been evaluated in a damage detection problem of a reinforced concrete frame experimentally tested under different levels of damage.

Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models

2014 ◽  
Vol 4 (1) ◽  
pp. 52-68 ◽  
Author(s):  
Hong-Kui Pang ◽  
Hai-Wei Sun
Keyword(s):  
Stochastic Volatility ◽  
Temporal Integration ◽  
Time Integration ◽  
Computational Cost ◽  
Jump Diffusion ◽  
Integration Scheme ◽  
Arnoldi Method ◽  
Exponential Time ◽  
Jump Diffusion Model ◽  
Exponential Time Integration

AbstractThe stochastic volatility jump diffusion model with jumps in both return and volatility leads to a two-dimensional partial integro-differential equation (PIDE). We exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as the action of an exponential of a block Toeplitz matrix on a vector. The shift-invert Arnoldi method is employed to approximate this product. To reduce the computational cost, matrix splitting is combined with the multigrid method to deal with the shift-invert matrix-vector product in each inner iteration. Numerical results show that our proposed scheme is more robust and efficient than the existing high accurate implicit-explicit Euler-based extrapolation scheme.

Numerical and Analytical Modeling of Unbonded Flexible Risers

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
A. Bahtui ◽  
H. Bahai ◽  
G. Alfano
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Computational Cost ◽  
Element Model ◽  
Integration Scheme ◽  
Element Analysis ◽  
Axial Tension ◽  
External Pressures ◽  
Time Integration Scheme ◽  
Flexible Risers

This paper presents an analytical formulation and a finite element analysis of the behavior of multilayer unbonded flexible risers. The finite element model accurately incorporates all the fine details of the riser that were previously considered to be important but too difficult to simulate due to the significant associated computational cost. All layers of the riser are separately modeled, and contact interaction between layers has been accounted for. The model includes geometric nonlinearity as well as frictional effects. The analysis considers the main modes of flexible riser loading, which include internal and external pressures, axial tension, torsion, and bending. Computations were performed by employing a fully explicit time integration scheme on a parallel 16-processor cluster of computers. Consistency of simulation results was demonstrated by comparison with those of the analytical model of an identical structure. The close agreement gives confidence in both approaches.

On the Dynamic Response of Flexible Risers Caused by Internal Slug Flow

2012 ◽  
Author(s):  
Arturo Ortega ◽  
Ausberto Rivera ◽  
Ole Jørgen Nydal ◽  
Carl M. Larsen
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Slug Flow ◽  
Time Integration ◽  
Flow Dynamics ◽  
Two Phase ◽  
Structural Dynamic ◽  
Linear Finite Element ◽  
Flow Through ◽  
Flexible Risers

Slug flow through flexible risers is a frequent phenomenon which occurs during production of a mixture of oil and gas. The dynamic nature of the slug pattern induces time varying forces, which leads to structural vibrations of the riser. These vibrations can produce large deflections and stresses, which can leave it to fail by fatigue, excessive bending or local buckling. In this work the influence from slug flow on the structural dynamic response of a lazy wave flexible riser is analyzed using a computational tool consisting of one program for calculation of slug flow dynamics, and another program for structural dynamic response. Both programs apply a time integration method, and since slug flow will lead to dynamic motion response of the riser, and riser motion dynamics will influence slug flow dynamics, the two codes need to exchange information during the integration process. Information exchange is established by making a federation based on High Level Architecture (HLA). The federation is composed of SLUGIT and RISANANL. SLUGGIT is a two-phase flow code written in C++ which simulates dynamic slug flow through pipes and riser using a Lagrangian tracking model. RISANANL is a FORTRAN program for static and dynamic structural analysis of slender marine structures based on a finite element formulation. Using the HLA standard these two programs can carry out synchronized time integration and exchange information for each time step. In this work the structural analysis code accomplishes the dynamic response using a linear finite element (FE) formulation. Hence, forces from centripetal acceleration of the internal flow, relative velocity between the riser and surrounding water, and varying gravity of the pipe and content will be accounted for in the dynamic analysis. Displacements, stresses, internal pressure, and outlet flow rates of liquid and gas will be accounted for. The results encourage us to carry out a fully non-linear finite element analysis, in order to have a better understanding of the dynamic behaviour of flexible risers undergoing an unsteady internal two-phase flow.

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