Determining the conditions for stability of elevated pipelines on supports while pigging

Determining the conditions

for stability of elevated

pipelines on supports while

pigging

by Dr V.M.Varshitsky*, Dr A.A.Bogach,

Dr O.A.Kozyrev, and Dr I.B.Lebedenko

Strength Analysis Laboratory, Pipeline Transport Institute

(PTI, LLC), Moscow, Russian Federation

T

HE AIM OF the present study is to determine the maximum allowable pig-running speed which guarantees that the design position of above-ground sections of elevated pipelines is maintained during pigging or liquid cleaning. This paper presents the results of 3D computer modelling, showing the strain in an elevated expansion loop of a pipeline due to the impact of the inertia load during pigging or liquid slug running.

The strain in the elevated expansion loop sections of the pipeline was modelled using the finite-element method in the LS-DYNA and ANSYS software packages.

Calculations were made for four standard sections of pipeline with expansion loops. As a result, the extent of displacements could be determined for elevated pipelines. The modelling results were used to calculate the maximum pig-running speed at which the design position of the elevated pipeline is maintained.

This article compares the results of calculations made using engineering techniques with those made using computer 3D modelling methods. It also presents a comparison of computer modelling performed using the ANSYS and LS-DYNA software packages.

Key words: stress-strain state, finite-element method, supports, pig running speed, expansion loop, bend.

Corresponding author’s contact details: email: varshitskiivm@niitnn. transneft.ru

C

ONSTRUCTING PIPELINES IN

AREAS with varying engineering and geological conditions, due to alternating thawed and frozen soils, necessitates laying the pipeline above ground. The above-ground or elevated pipeline is a pipeline laid on supports of various designs, and the structure of these pipelines includes the compensator or the expansion loop section, built using bends [1].

Due to these expansion-loop sections with bends in the elevated part of the pipeline, the movement of pigs at speeds exceeding permissible rates can cause the pipeline to be displaced beyond acceptable limits at the bends, or cause the pig to be damaged [2-5].

sections on supports is maintained during pigging.

Various studies [6, 7] have examined methods of calculating the parameters of pig movement through a pipeline, in order to monitor the movement of various types and sizes of pig, in areas with varied terrain, pipeline operating conditions, and pumped product properties. However, the allowable pig-running speed has not been assessed in terms of the stability of elevated pipelines on supports.

In this study, the allowable pig-running speed was calculated using two methods. The first method assumes an engineering approach, while the second models the interaction of moving loads with curved sections of elevated pipeline using software systems based on the finite-element method (FEM). The interaction of moving loads with curved sections of elevated pipeline was modelled using ANSYS and LS-DYNA software packages in a linear-elastic problem setting.

Figure 1 presents a diagram of a standard pipeline section with a strain expansion loop: the fixed supports prevent any pipeline displacement; the free-moving supports do not allow the pipeline to shift downwards; the longitudinally-moving supports prevent the pipeline from moving horizontally and downwards.

The initial data used for the calculations included:

• external pipeline diameter • pipeline wall thickness • bend wall thickness

• density of the transported product in normal operating conditions • density of the transported product

in test conditions • soil parameters • pipe material • temperature drop • internal pressure • support-block mass

• thermal-insulation thickness

• density of thermal-insulation material

• casing thickness

• density of casing material • static-friction factor • sliding-friction factor

The following loads were taken into account when making the calculations:

• pipeline weight • insulation weight • casing weight • oil weight

• weight of pig and removed liquid slug, which are considered as concentrated masses distributed along the length and which travel according to the speed of the pig • inertial load as the pig passes

through the curved sections, which was accounted for by introducing a distributed inertial load according to the formula:

F MLV

R

= 2 (1)

where:

M = unit length mass of the moving device

L = finite-element length

V = speed at which the device moves

R = radius of the curved section (the load direction is perpendicular to the tangent of the curved section)

Also considered are:

• the internal pressure • the temperature drop

• the friction force, based on the Coulomb friction model.

To determine the impact pipeline-inspection devices can have on changes to the stress-strain state of pipelines, the oil mass was calculated for a length equal to that of the device, and was compared with the mass of the device (Tables 1 and 2).

18м 1 2

20,3м

28,7м

500м 3

4

5 6

7

8 9 10

18м 18м 18м 18м 18м 18м

Fig.1. Diagram of a standard pipeline expansion loop: - fixed support;

- free-moving support; - longitudinally-moving support

Pig type Length, mm Oil mass, kg Device mass, kg Device mass per _{metre, kg/m}

Single-channel geometry pig 3210 2194 820 255.5

Multi-channel geometry pig with

navigation system 2418 1653 800 330.9

Inspection pig for determining pipeline

position 3186 2178 1200 376.7

Ultrasonic inspection pig 4710 3220 1850 392.8

Magnetic-flux-leakage inspection pig 4250 2905 3550 835.3

Integrated magnetic inspection pig 4964 3393 6000 1208.7

Integrated magnetic-ultrasonic

inspection pig 8130 5557 6100 750.3

Table 1. Comparison of the oil mass and the mass of a pipeline-inspection device with equal length and 1020 mm (40 in) diameter.

Pig type Length, mm Oil mass, kg Device mass, kg Device mass per _{metre, kg/m}

Single-channel geometry pig 2500 1105 300 120

Multi-channel geometry pig with

navigation system 2595 1147 736 283.6

Inspection pig for determining pipeline

position 3560 1574 1010 283.7

Ultrasonic inspection pig 4360 1927 2100 481.7

Magnetic-flux-leakage inspection pig 5550 2453 4250 765.8

Integrated magnetic inspection pig 6000 2652 2790 465

Integrated magnetic-ultrasonic

inspection pig 2500 1105 300 120

Parametric engineering method

of calculation

In order to calculate allowable pig-running speed at bends, a parametric engineering methodology was developed, as applied to a standard expansion loop section (Fig.1).

A pipeline will shift when the force acting on a support while a pig passes through a curved section is greater than the frictional force:

F F

>

_{f (2)}

The frictional force in the supports is calculated using the formula:

Ff = µR (3)

where µ is the (static) friction factor between the support’s bench and its base, and is equal to 0.15, and R is the force of the support’s reaction.

R= Mg

cosφ (4)

where

g = gravitational acceleration

ϕ = the pipeline’s angle of incline relative to the horizon, which is equal to 0°

М = the mass acting on the support. M m= _@+m_ins+m_prod+m_sb+m_PD

(5) where

m_p = the mass of the pipe steel

m_ins = the mass of the insulating coating

m_prod = the mass of the pumped product

m_psb = the mass of the support block

m_PD = the mass of the pigging device The mass of pipeline steel:

m_p =ρ_stl Dπ −d

4( 2 2) (6)

where

r_st = the steel density

l = the sum of half-lengths of the spans on both sides of the support

D = pippeline external diameter

d = pipeline internal diameter The mass of the insulating coating is:

mins =mtio +mc (7)

where

m_ti = the mass of thermal insulation

m_c = is the mass of the protective casing

The mass of the pigging device is taken to be dependent on the technological process. When calculating the final stage of water displacement, the mass of the device is equivalent to the mass of the water slug inside a 10m-long pipeline:

m_ws = ρ_{w w}l πd

4

2 ₍₈₎

where

r_w = the water density

l = the length of the water slug within the pipeline

d = the internal diameter of the pipeline.

In order to calculate allowable pig-running speed for the section under consideration, frictional and displacement forces acting on supports 2 and 3 are determined as the device runs through the pipe.

Determining the gravitational force acting on supports 2 and 3:

1. The pig begins to move from the beginning of the bend:

The motion is described by Equns 9 - 12 (see right).

2. The pig is between the second and third supports:

The motion is described by Equns 13 and 14 (see right).

PP t R X t

Fskr X t R X t X t R X t

1 1 2

2 1 2

2 2 1 2 2 ( ) : ( ) ( ) ( ) ( ) ( = ( − )× + −     

 + −₂ )) 3 1 ₂2( )

3 + ( − )       ×               + + +

R X t

Lskr RI (Mtr Mtepl Mkojj Mloj g+ )×

PP t X t R

Fskr R R X t R R R X t R

2 1 1

4 1 1 1

2 4 1

1 2 ( ) : ( ) ( ) ( ) = ( − )× − − −  

 _ − − ₂− 11 3 1 ₂ 1 4 13

   _ + ( − )       × −               +

X t R

Lskr R R Mt

( )

( ) ( rr Mtepl Mkoj Mloj g+ + + )× (10)

(9)

V11( ) :t =PP t1( )+PP t2( ) (11)

V t X t R

Fskr X t R X t R R R X

12 1 1

1 1

2

1 1

2 3 4 1

1 2 ( ) : ( ) ( ) ( ) =

(

−

)

× −    _ − + − − (( ) ( ) t R

Lskr R R Mtr Mtepl

−           × −               + + + 1 2

4 13

(

MMkoj Mloj g+

)

× (12)

V t

Fskr R X t Lskr R X t Lskr X

21

4 1 ₂ 2 4 1 ₂ 3 2

( ) : ( ) ( ) ( = − +  

 _ _ − + _ + tt R Lskr

R R Mtr Mtepl M

) ( ) − +    _       −               + + + 1 ₂

4 13 ( kkoj Mloj g+ )×

V t

Fskr X t R Lskr X t R Lskr R

22

2 1

2 2 1 2 3 4

2 ( ) : ( ) ( ) = − +  

 _ _ − + _ + −XX t Lskr

R R Mtr Mtepl M

1 2

4 13

( ) ( ) +    _    _ −              

+( + + kkoj Mloj g+ )×

(13)

(14)

V t R X t

Fskr R X t R X t R R

31 4 2

4 2

2

4 2

2 3 4

2 ( ) : ( ) ( ) ( ) = ( − )× − ( )  

 _ − + − 11 4 2 2 4 13

− −    _    _ × −               + +

R X t

Lskr R R Mtr Mt

( )

( ) ( eepl Mkoj Mloj g+ + )× (15)

PP t R X t

Fskr R R R X t R R R X

31 4 2

4 1 4 2

2 4 1

4 2 2 ( ) : ( ) ( ) ( = ( − )× − − −  

 _ − − − tt R X t

Lskr R R Mtr

) ( )

( )

2 3 4 2 2 4 13

+  −   _       × −              

+( ++Mtepl Mkoj Mloj g+ + )×

PP t X t R Fskr R R

X t R _{R R} X t

32 1 4 5 4

1 4

2 5 4 1

2 ( ) : ( ) ( ) ( ) = ( − )× − − −  

 _ − − −RR X t R

Lskr R R Mtr Mtepl

4

2 3 1 2 4

5 43

+ −     × −               + + ( )

( ) ( ++Mkoj Mloj g+ )×

(16)

(17)

V32( ) :t =PP31( )t +PP32( )t

V41( ) :t =0

V t

Fskr R X t Lskr R X t Lskr X

42

5 1

2 5 1 2 3 2

2 ( ) : ( ) ( ) ( = − +  

 _ _ − + _ + tt R Lskr

R R Mtr Mtepl M

) ( ) − +    _    _ −               + + + 4 2

5 43 ( kkoj Mloj g+ )×

(18)

3. Part of the pig has passed the third support:

The motion is described by Equns 15 - 18 (see previous page).

4. The pig is between the third and fourth supports:

The motion is described by Equns 19 and 20 (see previous page). where

PP = components of the loads acting on the supports

V = the gravitational force acting on the supports

R0, R1, R2, R3, R4, R5 = the coordinates of the principal points in the section (Table 1)

X1(t), X2(t) = the pig coordinates at a moment in time

Fskr = the vertical force of the pig

Lskr = the length of the pig

Mtr = the mass of the pipeline

Mtepl = the mass of the thermal insulation

Mkoj = the mass of the casing

Mloj = the mass of the support block

g = gravitational acceleration

Determining the displacement force acting on supports 2 and 3 as a result of the pig passage:

1. The pig is located at support 2 and has entered the bend

The motion is described by Equn 21 (below).

2. The pig is between supports 2 and 3:

The motion is described by Equns 22 - 24 (below).

3. The pig is in the bend and has partially passed the support 3:

The motion is described by Equns 25 and 26 (below).

where

Fcentr = the displacement force from the pig’s passage

Fcentr t X t R Fskr Vskr

Lskr g Rotv

R R

11 1 2

4 2 ( ) := ( ( )− )× × × ×        ×

− 22 1 2

2 3 2 1

1 2

2 4 2

1 2 −( − )       ×  − +( − )      + − −

X t( ) R _{R R} X t( ) R _{R R} (X t( )−− )

             − ( )                 R R R 2 2 4 13

Fcentr t X t_{Lskr g Rotv}R Fskr Vskr

R R

12 1 2

2 2 ( ) := ( ( )− )× × × ×        ×

− 11 1 2

2 3 4 2

1 2

2 2 1

1 2 +( − )       × ( − )−( − )      + − +

X t( ) R _{R R} X t( ) R _{R R} X (tt R

R R )− ( )               − ( )                 2 2 4 13

Fcentr t R R Fskr Vskr

Lskr g Rotv

21 3 2

2 2 ( ) := ( − )× × × × ×        

Fcentr t R R Fskr Vskr

Lskr g Rotv

22 3 2

2 2 ( ) := ( − )× × × × ×        

Fcentr t R X t Fskr Vskr

Lskr g Rotv

R R

31 3 1

4 2 ( ) := ( − ( ))× × × ×        ×

− 33 3 ₂1 3 3 1 3 ₂1 4 3 3 2 +( − )       × ( − )−( − )      + − + −

R X t( ) _{R R} R X t( ) _{R R} R XX t

R R

1 2 4 13

( ) ( )               − ( )                

Fcentr t R X t Fskr Vskr

Lskr g Rotv

R R

32 3 2

3 2 ( ) := ( − ( ))× × × ×        ×

− 11 3 2

2 3 4 3

3 2

2 3 1

2 ( )−( − )       × ( − )+( − )      + ( − )

R X t

R R R X t R R

( ) ( )  ₋₋( − )              − ( )                

R X t

R R

3 2 2 4 13

Lskr = the length of the pig

Vskr = the pig running speed

Rotv = the radius of the bend

Table 3 presents the results of calculating frictional force in supports for a 1020-mm diameter pipeline. In calculations, the pig-running speed was taken to be 7 m/s, while the following were used as time-reference points: 0, 0.5 s, 1 s, 1.5 s, 2 s, and 2.5 s.

The results of displacement force calculations for supports 2 and 3 are presented in Table 4.

By comparing values for the frictional force (Table 3) and displacement force (Table 4) acting on supports 2 and 3, it may be concluded that at speeds above 7 m/s the pipeline will exceed frictional force during pigging, and will shift relative to its design position. Thus pigging for the given pipeline is permissible at speeds under 7 m/s.

Calculating displacements

for elevated pipelines

The interaction of a moving load with

the curved section of an elevated pipeline was modelled using the ANSYS and LS-DYNA software packages in the linear-elastic problem setting. Calculations were performed with several variants and for four representative pipeline expansion-loop sections, and the allowable pig-running speeds were determined. Dynamic numerical spatial models were developed to show the displacement of the elevated pipeline sections due to pig running.

The ANSYS calculation scheme includes finite pipe elements of the PIPE type, which account for the internal pressure in the pipeline; and finite contact elements CONTA178, which model the friction during pipeline displacement along the supports. The contact type is node-to-node. The static friction factor between the base and the bench of the support is assumed to be 0.15, while the sliding friction factor is assumed to be 0.1. The entire temperature-expansion section (the pipeline section with an expansion loop between fixed supports) is included in the design model.

The pig’s run through a standard trapezoid expansion loop section was also

Time, s Frictional force on support 2, kN Frictional force on support 3, kN

0 30.59 10.37

0.5 29.41 12.01

1 15.72 15.72

1.5 12.01 29.41

2 10.37 30.59

2.5 10.03 29.57

Table 3. Frictional forces in the supports 2 and 3.

Time, s Displacement force on _{support 2, kN} Displacement force on _{support 3, kN}

0 0 0

0.5 13.807 12.183

1 14.851 14.851

1.5 0 0

2 0 0

2.5 0 0

modelled using the finite-element method (FEM) in the dynamic mode in the LS-DYNA software package. LS-LS-DYNA modelling was performed in order to verify the calculation method developed in the ANSYS software package, and described above. The expansion-loop section, straight sections of pipeline,

Fig.2 (above). Diagram of the strained and unstrained expansion-loop section at 5.1 secs, calculated in the LS-DYNA software package.

Fig.3 (below). Diagram of the strained and unstrained expansion-loop section at 8.1 secs, calculated in the LS-DYNA software package.

Support LS-Dyna ANSYS

1

10

Table 5. A comparative analysis of lateral displacements relative to the initial axis of the elevated pipeline on supports, calculated using LS-DYNA and ANSYS software packages.

and connections were modelled using shell finite elements (FE), with element-thickness parameters and geometric dimensions specified according to the initial data. The mass of moving parts in the supports was taken into account by introducing concentrated masses into the model of the pipeline at the locations of the free-moving supports.

The vertical displacement of the pipeline and of the expansion loop section under the impact of gravity was limited in sections with free-moving supports through the use of contact support , with Coulomb friction taken into account.

Fixed supports and longitudinally-moving supports were modelled with the limitation of the relevant nodal degrees of freedom.

The calculation was performed assuming the linear-elastic behaviour of the pipe, pig, and liquid slug materials (i.e. up to the yield point).

LS-DYNA modelling was performed in two stages:

• Stage 1: establishing a stationary state in the pipeline and expansion loop section, within the gravity force field prior to pigging. At this stage of modelling, the batching pig and the liquid slug are motionless at 2 m from the entrance to the expansion-loop section.

• Stage 2: the run of the batching

pig and the liquid slug through the expansion loop section at a set speed. The expansion-loop section is at the stress-strain state found in stage 1.

Figures 2 and 3 present strain diagrams for the expansion loop section as the liquid slug and the pig pass through it.

Table 5 presents a comparative analysis of lateral displacements relative to the initial axis of the elevated pipeline on supports, calculated using LS-DYNA and ANSYS software packages. These calculations were performed using the LS-DYNA and ANSYS software packages, which operate independently of one another. A comparison of their results shows

Fig.4 (above). Design model for standard section 1.

Fig.5 (right). Diagram for displacement vectors at supports. UX - longitudinal displacements along the pipeline’s initial axis; UY - lateral displacements perpendicular to the pipeline’s initial axis.

Fig.6 (below). Initial and displaced

satisfactory congruence, indicating the accuracy of the methodology developed here.

Calculation results for variants

using the ANSYS software

Calculations were made for several variants: slugs of 10, 15, and 20 m in length, moving at speeds of 7 and 10 m/s (6 variants). Motion was also calculated for an inspection pig with length 4.96 m and weight 6 tonnes (for a 1020-mm pipeline), and for a 5.55-m long inspection pig, weighing 4.25 tonnes (for a 820-mm pipeline), moving at speeds of 7 and 10 m/s (2 variants).

Calculation for standard section 1,

with pipeline diameter 1020 x 12 mm

Figure 4 presents the design model for standard section 1; the legend is that used in Fig.1.

Figure 6 shows the initial position of standard section 1 and its displaced position after the water slug and pig with total length of 20 m have run through, at a speed of 10 m/s.

Table 6 presents the maximum longitudinal and lateral displacements for the elevated pipeline on supports at the standard section1, relative to its initial axis (with support number shown), when

Fig.7. Plan of standard section 2.

water slugs of length 10, 15, and 20 m pass through it.

Table 7 presents the maximum longitudinal and lateral displacements for the elevated pipeline on supports at standard section 1, relative to its initial axis (with support number shown) due to the impact of the moving load (the pig).

Calculation for standard section 2,

with pipeline diameter 1020 x 12 mm

Figure 7 presents the design model for standard section 2; the legend is that used

in Fig.1. Figure 8 shows the initial and displaced positions of standard section 2 after the water slug and pig with total length of 20 m have run through at a speed of 10 m/s.

Table 8 presents the maximum longitudinal and lateral displacements for the elevated pipeline on supports at standard section 2 relative to its initial axis (with support number shown) as water slugs with length 10, 15, and 20 m pass through it.

Table 9 presents the maximum

Speed, m/s

Length of the displaced water slug, m

10 15 20

UX, m UY, m UX, m UY, m UX, m UY, m

7 1.8 x 10-3

(support 9)

1.8 x 10-3

(support 8)

1 x 10-3

(support 3)

1.25 x 10-3

(support 2)

1.1 x 10-3

(support 9)

1.5 x 10-3

(support 8)

10 0.26

(support 9)

0.4 (support 8)

0.35 (support 9)

0.53 (support 8)

0.39 (support 9)

0.58 (support 8)

Speed,

m/s UX, m UY, m

7 _{(support 3)}0.015 _{(support 6)}0.048

10 _{(support 3)}0.037 _{(support 6)}0.068

Table 6 (above). Maximum displacements for an elevated pipeline at standard section 1 as the water slugs pass through it (the UX, UY displacement vector directions correspond to Fig.5).

Table 7 (right). Maximum displacements for the elevated pipeline on supports at standard section 1 during pigging (the UX, UY displacement vector directions correspond to Fig.5).

Speed, m/s

Length of the displaced water slug, m

10 15 20

UX, m UY, m UX, m UY, m UX, m UY, m

7 2.1 x 10-3

(support 8)

2.2 x 10-3

(support 6)

4.2 x 10-3

(support 4)

4.3 x 10-3

(support 5)

5.6 x 10-3

(support 8)

8 x 10-3

(support 0)

10 0.44

(support 8)

0.48 (support 9)

0.7 (support 8)

0.78 (support 9)

0.8 (support 8)

0.88 (support 9)

Speed,

m/s UX, m UY, m

7 _{(support 9)}0.009 _{(support 1)}0.019

10 _{(support 4)}0.02 _{(support 6)}0.024

Table 8 (above). Maximum displacements for the elevated pipeline on supports at standard section 2 as the water slugs pass through it (the UX, UY displacement vector directions correspond to Fig.5).

longitudinal and lateral displacements for the elevated pipeline on supports at standard section 2 relative to its initial axis (with support number shown) due to the impact of the moving load (pig).

Calculation for standard section 3,

with pipeline diameter 1020 x 12 mm

Figure 9 shows the design model for

standard section3. The legend is that used in Fig.1. Figure 10 shows the initial and displaced positions of standard section 3 after the water slug and pig with total length of 20 m have run through at a speed of 10 m/s.

Table 10 presents the maximum longitudinal and lateral displacements for the elevated pipeline on supports at

Fig.9 (above). Plan for standard section 3.

Fig.10 (right). Initial and displaced positions of standard pipeline section 3 after the water slug and pig with total length of 20 m have run through at a speed of 10 m/s (scale 53).

Speed, m/s

Length of the displaced water slug, m

10 15 20

UX, m UY, m UX, m UY, m UX, m UY, m

7 2.6 x 10-3

(support 7)

4.5 x 10-3

(support 7)

1 x 10-3

(support 5)

1.25 x 10-3

(support 4)

1.3 x 10-3

(support 5)

2.2 x 10-3

(support 4)

10 0.24

(support 4)

0.32 (support 2)

0.32 (support 4)

0.44 (support 2)

0.36 (support 8)

0.49 (support 9)

Speed,

m/s UX, m UY, m

7 _{(support 3)}0.021 _{(support 6)}0.032

10 _{(support 3)}0.048 _{(support 6)}0.07

Table 10 (above). Maximum displacements for the elevated pipeline on supports at standard section 3 as the water slugs pass through it (the UX, UY displacement vector directions correspond to Fig.5)

Table 11 (left). Maximum displacements for the elevated pipeline on supports at standard section 3 during pigging (the UX, UY displacement vector directions

standard section 3, relative to its initial axis (with support number shown) as water slugs with length of 10, 15, and 20 m pass through it.

Table 11 presents the maximum

longitudinal and lateral displacements for the elevated pipeline on supports at standard section 3 relative to its initial axis (with support number shown) due to the impact of the moving load (pig).

Fig.11 (above). Plan for standard section 4.

Fig.12 (left). Initial and displaced positions of standard pipeline section 4 after the water slug and pig with total length of 20 m have run through at a speed of 10 m/s (scale 43).

Speed, m/s

Length of the displaced water slug, m

10 15 20

UX, m UY, m UX, m UY, m UX, m UY, m

7 3.8 x 10-3

(support 8)

6.7 x 10-3

(support 7)

1.65 x 10-3

(support 5)

2.2 x 10-3

(support 4)

2.25 x 10-3

(support 5)

2.7 x 10-3

(support 4)

10 0.25

(support 4)

0.32 (support 2)

0.33 (support 4)

0.45 (support 2)

0.36 (support 4)

0.48 (support 2)

Speed,

m/s UX, m UY, m

7 _{(support 9)}0.008 _{(support 1)}0.018

10 _{(support 4)}0.054 _{(support 7)}0.1

Table 12 (above). Maximum displacements for the elevated pipeline on supports at standard section 4 as the water slugs passes through it (the UX, UY displacement vector directions correspond to Fig.5).

Calculation for standard section 4,

with pipeline diameter 820 x 9 mm

Figure 11 shows the design model for standard section 4; the legend is that used in Fig.1. Figure 12 shows the initial and displaced positions of standard section 4 after a water slug and pig with total length of 20 m have run through at a speed of 10 m/s.

Table 12 presents the maximum longitudinal and lateral displacements for the elevated pipeline on supports at standard section 4 relative to its initial axis (with support number shown) as water slugs with length of 10, 15, and 20 m pass through it.

Calculations were performed for the inspection pig with length 5.55 m and weight 4.25 tonnes (Table 2), moving at speeds of 7 and 10 m/s (2 variants).

Table 13 presents the maximum longitudinal and lateral displacements of the elevated pipeline on supports at standard section 4, relative to its initial axis (with support number shown) due to the impact of the moving load (pig).

Conclusions

1. The calculations made for four standard expansion-loop sections of oil pipeline with diameters of 1020 mm and 820 mm during pigging have shown that where pig speed is no more than 7 m/s, the design position of the elevated pipeline on supports is maintained, both during water displacement and during the inspection pig run.

2. Comparing the results of calculations from two independent software packages, LS-DYNA and ANSYS, shows that their results correspond satisfactorily, which indicates the accuracy of the developed methodology.

3. Comparing allowable pig-running speeds calculated using engineering practice with those calculated using the ANSYS software package has shown that permissible speeds coincide for a standard expansion loop with 1020 mm diameter, where 10-m liquid slug is displaced.

4. In several cases, the results of allowable pig-running speed calculations obtained through theoretical methodology and from the ANSYS software package showed sharp discrepancies. This is due to the fact that the theoretical methodology is based on a set of assumptions which do not allow the behaviour of a structure during pigging to be accurately assessed.

References

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Y.Feng, and W.Yubin, Analyzing the crash between gauging pig and the elbows of u-shaped pipeline, Proc. 9th International Pipeline Conference IPC2012, Calgary, Alberta, Canada (September 2012). 3. F.Esmaeilzadeh, D.Mowla, and M.Asemani,

Mathematical modeling and simulation of pigging operation in gas, Engineering 69 (2009) pp 100-106.

4. K.K.Botros and H.Golshan, Dynamics of pig motion in gas pipelines [C], AGA Operation conference & Biennial exhibition, Pittsburgh, Pennsylvania, Session 11: Corrosion Control, (May 2009).

5. L.Matthews and M.Kennard, Velocity control of pigs in gas pipelines, In: Pipeline Pigging & Integrity Technology, 3rd _{Edn, Ed. John Tiratsoo, Clarion} Technical Publishers, Houston, TX, USA, (2003) pp 35-47.

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