class 10 - free span analysis

8/10/2019 Class 10 - Free Span Analysis

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Pipeline Free Span Analysis

Dr. Ir. Ahmad Taufik

(SUBSEA PIPELINE ENG.)


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Introduction

Pipeline spanning can occur when the contact between the pipeline

and seabed is lost over an appreciable distance on a rough seabed.

This will cause to static overload and thus overstress of pipeline

section due to bending stress and lead to the pipeline deformation or

crack. The condition, under right current speed, pipeline span length and

weight will also causing vortex induce vibration VIV that may lead to

fatigue failure.

The discussion will focus will design how to avoid this possible

occurrence by calculating the allowable freespan in terms of staticand dynamic loading.

The vortex shedding induced oscillations due to currents is the most

deepwater pipelines limiting factor for the allowable span length.


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Pipeline Integrity Management System

Offshore Pipeline and Risk

Associated with it

Free Span Lead to Bending


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Other Possible

Problems related

to Freespan


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Problem Description

FreespanFreespan can result in failure of pipelines due to excessive yielding and

fatique. It may also cause interference with human activities such as

fishing. Freespan can occur due to unsupported weight of the pipeline

section and dynamic loads from waves and currents.

Vibration :

1. In Line Vibration

2. Cross Flow Vibration

INLINE OSCILLATION

ARAH

ALIRAN

VORTEX

CROSS FLOW OSCILLATION

PIPA

PIPA


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tot

e

aDW

IC

L

2

Problem Description - Static Analysis

La = Allowable static freespan

C = end restrained constant

= 9.87 for pinned-to-pinned conditionI = Moment of inertia

e = Equivalent stress (Von Misses)

W = Uniformly distributed load per unit length

22

)( IDs FFW

Freespan can result in failure of pipelines due to excessive yielding andfatique. It may also cause interference with human activities such as

fishing. For static loading the maximum allowable freespan subject to

static loading


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Pipeline Integrity Management System

Maximum Allowable Freespan Offshore Pipeline


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Problem Description Dynamic Analysis

Freespan can also vibrate due to interaction of unsupported weight ofthe pipeline section and dynamic loads from waves and currents.

Vibration :

1. In Line Vibration

2. Cross Flow Vibration

INLINE OSCILLATION

ARAH

ALIRAN

VORTEX

CROSS FLOW OSCILLATION

PIPA

PIPA


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Problem Description - Dynamic Analysis

A. In-Line Oscillations

The amplitude of the in-line motion is only 10% of those associated

with cross-flow motion. Several parameters are used in determining

the potential for vibration. These include the reduced velocity, Ur,

and the stability parameter, Ks.

The first and second modes of in-line instability are associated with

symmetrical vortex shedding and have a peak response at reduced

velocities (Ur) of 1.9 and 2.6, respectively.

To prevent this in-line response at either mode of vortex shedding

excitation, stability parameter (Ks) > 1.8(Wotton, 1991). DnV also state that the resonant in-line vortex shedding induced

oscillation may occur when 1.0 < Ur < 2.2, the shedding will be

alternate.


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B. Cross-Flow Oscillations

Excitation in the cross-flow direction is potentially more dangerous

than that in-line since amplitudes of response are much greater than

those associated with in-line motion. However, these oscillation occur at much larger velocities than in-

line oscillations and are not normally governing. The limiting value

for cross-flow oscillations based on DnV is Ks< 16.

Problem Description - Dynamic Analysis


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Design Consideration

Dynamic Stresses

The presence of bottom currents can cause significant dynamic

stresses, if fluid structure interaction (vortex shedding) in these free-

span areas causes the pipeline to oscillate. These oscillations can result in fatique of the pipeline welds, which

can reduce pipeline life. The frequency of vortex shedding is a

function of the pipe diameter, current velocity, and Strouhal Number.


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Vortex-Shedding Frequency

The vortex-shedding frequency is the frequency at which pairs of vortices are shed

from the pipeline and is calculated based on the following:

where:

fs= vortex-shedding frequency

S= Strouhal Number

Uc= design current velocity

D= pipe outside diameter

Strouhal Number is the dimensionless frequency of the vortex shedding and its afunction of the Reynolds Number. Reynolds Number Reis a dimesionless parameter

representing the ratio of inertial force to viscous force:

where vis kinematic viscosity of fluid (1.2 x 10-5 ft2/sec for water at 60F).


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Pipeline Natural Frequency

The natural frequency for vibration of the pipe span is given by the following formulas:

where

fn= pipe span natural frequency

Ls= span length

Me= effective mass

Ce= end condition constant

The end condition constant reflect the support conditions of the pipeline span.

Ce= (1.00 )2= 9.87 (pinned-pinned)

Ce= (1.25 )2= 15.5 (clamped-pinned)

Ce= (1. 50 )2= 22.2 (clamped- clamped)


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Pipeline Natural Frequency

The effective mass is the sum of total unit mass of the pipe, the unit mass of the pipe

contents, and the unit mass of the displaced water (added mass).

whereMp= unit mass of pipe including coating (slug/ft or kg/m)

Mc= unit mass of pipe of content (slug/ft or kg/m)

Ma= added unit mass (slug/ft or kg/m)

The added mass is the mass of water displaced by the pipeline and is calculated based

on the following:

where is mass density of fluid around the pipe (seawater = 2 slug/ft3or 1025 kg/m3).


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Reduced Velocity

The reduced velocity, Ur, is the velocity at which vortex shedding induced oscillations

may occur :

Figure 1 presents the reduced velocity for cross-flow oscillations based on the

Reynolds Number (DnV, 1981). Figure 2 presents the reduced velocity for in-line

oscillations based on the stability parameter (Ks).


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Figure 1. Reduced velocity for cross-flow oscillations

based on the Reynolds Number


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Figure 2. Reduced velocity for in-line oscillations

based on the stability parameter


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Stability Parameter

A significant for defining vortex-induced motion is the stability parameter, Ks, defined

as:

where sis logarithmic decrement of structural damping (= 0.125).


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Critical Span Length

The critical span length or the unsupported pipeline length at which oscillations of the

pipeline occur for a specific current is based on the relationship between the natural

frequency of the pipe free span and the reduced velocity.

The critical span length for cross-flow motion is:

The critical span length for in-line motion is :


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Design Criteria

General Considerations

For preliminary design purposes, it is customary to design a pipeline

such that at no location along the pipeline route does the

unsupported pipeline length exceed the critical span length for which

in-line motion occurs due to vortex shedding, at any time during thedesign life of the pipeline.

However, in deep water, where traditional deployment of span

supports is not possible, this conservative design procedure can be

quite costly (Why?)

Thus, the selection of the allowable span length can become a risk

assessment type solution.


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Design Criteria

Current Velocity Selection

The calculated reduced velocity, stability parameter, Reynolds

Number, and critical span length should all be based on current

velocity that is perpendicular to the pipeline.

This design current should be based on the 100-year near bottom

current unless otherwise directed.


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Design Criteria

End Condition Selection

The selection of the proper end conditions for the pipe free span has

a significant impact on the allowable span length selected.

The end condition selected can influence the calculated critical span

length by as much as 50 percent, thus making the selection of the

proper end conditions a critical step in selecting the proper allowable

span length.


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5.4 Design Criteria

5.4.4 Design Parameters

Two types of motions are created by vortex shedding. The design

engineer should only design the pipeline such that in-line motion is

allowed to occur after evaluating the possible economic impacts thata smaller allowable span length would create. Even after such a

decision has been made, the designer should undertake a fatigue

life analysis check.


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Design Steps

The following steps are based on the use of figure 1 and 2 to assist in

determining the allowable pipeline free span length.

Step 1: Determine the design current (100-year near bottom

perpendicular to the pipeline)

Step 2: Calculate the effective unit mass of the pipelineStep 3: Calculate Reynolds Number

Step 4: Calculate stability parameter

Step 5: Using the stability parameter enter Figure 2 to determine the

reduced velocity for in-line motion.Step 6: Using the stability parameter enter Figure 1 to determine the

reduced velocity for cross-flow motion.


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Design Steps

Step 7: Based on the terrain and conditions involved, determine the

type of free span end conditions and calculate the end condition

constant.

Step 8: Calculate the critical span length for both in-line and cross-flow

motionStep 9: For the majority of projects, the allowable span length is the

critical span length calculated for in-line motion. However, when

economic factors warrant, the critical span length calculated for

cross-flow motion can be selected.

Step 10: When in-line motion is permitted, the fatigue life of the free

span should be calculated and evaluated for the pipeline.


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Example of Design Calculation

This example calculates the allowable span length to the cross-flow

oscillation based on the following information:

Outside diameter of pipe (D)

=

0.2757

m

Inside diameter of pipe (Di)

=

0.2509

m

Density of fluid in pipe (f) = 107 Kg/m3

Density of pipe (p) = 1024 Kg/m3

Mass of pipe and coatings (Mp) = 74 Kg/m

Kinematic viscosity of external fluid (vk) = 1.565 x10-6 m2/sec

Current velocity (Uc)

=

0.35

m/sConstant for clamped-pinned ends (Ce) = 15.4


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Design Calculation

Step 1 : Effective Mass


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Design Calculation

Step 2 : Stability Parameter

Step 3 : Reynolds Number

Step 4 : Reduced Velocities

Ur= 1.6 from Figure 2 for in-line motion

Ur = 5.0 from Figure 1 for cross-flow motion


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Design Calculation

Step 5 : Critical Span Length for Cross-Flow Motion

Step 6 : Critical Span Length for In-Line Motion


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Fatigue Analysis Guideline

The fatigue life equation presented in this section is based on the

Palmgren-Miner Fatigue Model, which uses an S-N model based on

the AWS-X modified curve of the form:


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Fatigue Analysis Guideline

Where:

Lf = fatigue life (years)

Ls = span length

Ds = outside diameter of steel

fn = pipe frequency (Hz)

f /fn = frequency ratio (Figure 3)

A/D = amplitude ratio (Figure 4)

Ti = current duration (hrs/day).

This simplified fatigue life equation is expanded as follows:


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Figure 3. Chart for determination of frequency ratio based on (V/ Dofn).


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Figure 4. Chart for determination of amplitude ratio

based on stability parameter(Ks).


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Fatigue Calculation Procedure

The following steps should be followed when checking the fatigue life of

free span length:

Step 1: Calculate the pipe natural frequency

Step 2: Determine the near bottom current velocity occurrencedistribution in histogram form using current duration blocks

Step 3: For each current segment determine the frequency ratio based

on (Uc/Dfn) and Figure 3.

Step 4: For each current segment determine the amplitude ratio based

on the stability parameter and Figure 4.

Step 5: Calculate the fatigue life


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Recommendation on Possible Pipeline Freespan

class 10 - free span analysis

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