Pipeline Calculations

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Pipeline Data

Pipeline Direction θ 90 deg

Outer Steel Diameter Ds 0,3415 m

Steel Thickness Tsteel 0,025 m

Concrate Thickness Tconcrate 0 m

Water Density ρ water 1025 kg/m3

Steel Density ρ steel 7850 kg/m3

Concrate Density ρ cancrate 2250 kg/m3

Content Density ρ content 820 kg/m3

Gravitation g 9,81 m/s2

Coating Data

Coating Thickness 1 Tcoat 1 0,0003 m

Coating Thickness 4 Tcoat 4 0 m

Coating Thickness 5 Tcoat 5 0 m

Coating Dencity 1 ρ coat 1 1300 kg/m3

Soil Interaction

Soil clay

Bottom Roughness zo 5,00E-06 silt and clay

Seabed Grain Size d50 0,0625 mm

Reduction Factor, Permeable Seabed τ perm,z 1

Friction Coefficient µ 0,2

Dry Unit Soil Weight Ys 18000 N/m3

Underained Shear Strength Su 10000 N/m3

Environmental Parameter

Spectral Spreading exponent 99

Reference Curret Height 3 m

Water Depth 100 m

Peak Enhancement Factor 3,3

Storm Duration 3 hours

Safety Class Factor

Wave and Current Data 1 Year 10 year 100 year

Hs (Tinggi Significant) 12 14 15

Tp(s) (Periode Signivicant) 12 15 18

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CALCULATION OF SPECTRAL JONSWAP  Outer Diameter :

OD = Ds + t.coat 1 + t.coat 2 + t.coat 3 OD = 0,3145 + 0,0003 + 0,0003 + 0,0024 OD = 0,3445 m  Reference period : Tn=

√

d g=

√

100 9.81=3.19 s  Peak Wave Frequency :

ω_p=2 π

T_p=

2 x 3.14

15 =0.42 rad /s ; Tp=15 s

Note : wave and current data for 10 years period  The Generalised Philips’ constant is given by :

γ 1−0.287 . ln¿ 5 6 Hs 2 ωp 4 g2 (¿¿)=

(

5 6 142x 0.424 9.812 (1−0.287 ln3.3 )

)

=0.01 α=¿  The spectral width parameter is given by :

σ =

{

0.07 if ω≤ ωp 0.09 else σ =0.09(ω>ωp) ω=2 π T_n= 2 x 3.14 3.19 =1.97

 The transfer function G transforms sea surface elevation to wave induced flow velocities at sea bed and is given by :

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G2(ω)= ω

sinh(kd)=

1.97−0.42 0.09 x0.42

)

2

]

S ηη( ω)=0.04

 The wave induced velocity spectrum at the sea bed SUU (ω) may be obtained

through a spectral transformation of the waves at sea level using a first order wave theory :

S uu( ω)=G2(_{ω ). S ηη(ω)}

S uu( ω)=1.82 x 0.04 S uu( ω)=0.14

 The spectral moments of n order is defined as :

M_n=

∫

0 ∞

ωn_S

UU(ω)dω

because we use order 0, so the value of the spectral moments is

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M₀=_0.14

We use order 2 to compare the spectral moments :

Mn=

∫

0 ∞

ωnSUU(ω) dω

M2=ω2x SUU=1.972x 0.14=0.54

 Therefore, the significant flow velociy amplitude at pipe level is :

U_s=2

_√

M₀

Us=2

√

0.04=0.75 m/s

 Mean zero up-crossing period of oscillating flow at pipe level is :

T_u=2 π

√

M0 M2 =2 x 3.14

√

0.04 0.54=3.19 s τ =T T_u= 15 3.19=4.7 LOADS CALCULATION

 The ratio between the design single oscillation velocity amplitude and the design spectral velocity amplitude for τ oscillations :

k_U=1 2

(

√

2 ln τ + 0.5772

√

2 ln τ

)

k_U=1 2

(

√

2 ln 4.7+ 0.5772

√

2 ln 4.7

)

k_U=_1.04 k_U=U ¿ U_s

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 Oscillatory velocity amplitude for single design oscillation, perpendicular to pipeline defined as :

−ln(5 x 10−6)

]

sin 90 ° V¿ =_{1.90 m/ s}

 Period associated with single design oscillation T¿=Tu=3.19 s

 Keulegan-Carpenter number for single design oscillation :

K¿ =U ¿ x T¿ D = 0.78 x 3.19 0.3445 =7.20

 Steady to oscillatory velocity ratio for design :

M¿ =V ¿ U¿= 1.90 0.78=2.44

 Cy _{is get from table 3-9 “Peak Horizontal Load Coefficient” (DNV RP F109}

page 25)

So, Cy=1.5

 Cz _{is get from table 3-9 “Peak Horizontal Load Coefficient” (DNV RP F109}

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Rasio antara design oscillation velocity amplitude dan design spectral velocity

amplitude untuk osilasi τ adalah :

k_U=U ¿ U_s= 1 2

(

√

2 ln τ + 0.5772

√

2 ln τ

)

So, Cy=1.03

Peak horizontal and vertical load are :

F_Y¿ =r_{tot , y}.1 2. ρw. D . CY ¿ .(U¿ +V¿ )2 F_Y¿ =1 .1 2.1025 . 0,3415 .1,5 . (0,78+1,9) 2 =_{1875,85 N/m} F¿_z =r_{tot, y}.1 2. ρw. D . Cz ¿ .(U¿ +V¿₎2 F_Y¿ =1 .1 2.1025 . 0,3415 .1,03 . (0,78+1,9) 2 =_{1288,08 N/m}

 Based on DNV E305, we find the value of submerged weight of pipeline by this formula :

W_s=

[

(

FD+FI

)

+μ . FL

μ

]

max

. F_w

using this formula to find the value of drag force, lift force and inertia force : Lift Force :

F_L=1

2. ρw. CLD

(

Us. cosθ+UC

)

2

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F_L=1 2x 1.025 x 0.9 x 0.3445 x 0.74 2 FL=4.40 N Drag force : F_D=1

2. ρw. CDD

|

(

Us. cos θ+UC

)

|

(

Uscos θ+Uc

)

; C_D = 0.7

FD= 1 2x 1025 x 0.7 x 0.3445

|

(0.74 )

|

(0.74) F_D=_{3.42 N} Inertia Force : F_I=π D 2 4 ρwCmAssin θ ; C_M = 3.29 where A_s=2 π Us Tu = 2 x 3.14 x 0.74 3.19 =1.46 So the inertia force is :

F_I=3.14 x 0.3445

2

4 x 1025 x 3.29 x 1.46 sin 90

°

F_I=_{40.18 N}

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W_s=

[

FD+FI+μ FL μ

]

max . F_w W_s=

[

3.42 x 40.18 x 0.2 x 4.40 0.2

]

x 1 W_s=_{2322.38 N} Desain Criteria : γ_sc=_1,83

(we use 1,83 because the storm duration (3 hours) is on extreme condition) G_c= Su D. γs Gc= 10.000 0,3445 .18.000 G_c=_1,61 F_c=W_S−F_z F_c=_{2322,38−1298,81} F_c=_{1023,57 N}

γ '_sc=_{13500 ; clay (very dense)}

K_c=Su. D

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K_c=10000 .0,3445 1023,57 Kc=3,37 FR=1023,57 . 4,1 .3,37 1,610,39 F_R=_{11722, 85 N} Criteria : γSC. F¿_γ +μ+F_Z¿ μ . w_S+F_R≤ 1 1,83. 1891,48+0,2+1298,81 0,2 .2322,38+11722,85≤ 1 0,31 ≤1 Vertical Stability γw b w_s+b≤1 1,1 936,79 2322,38+936,79≤1 0,32 ≤1

Based on above calculations, using two criteria for checking the stability the pipelines. The first criteria value is 0,31 ≤ 1.0 (fulfilled) and value

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of vertical stability is 0,32 ≤ 1.0 (fulfilled), so the conclusion of stability of pipelines is safe.