Pipeline Calculations

Pipeline Direction Outer Steel Diameter Steel Thickness Concrate Thickness Water Density Steel Density Concrate Density Content Density Gravitation

Pipeline Data θ Ds Tsteel Tconcrate ρ water ρ steel ρ cancrate ρ content g

90 0,3415 0,025 0 1025 7850 2250 820 9,81

deg m m m kg/m3 kg/m3 kg/m3 kg/m3 m/s2

Coating Thickness 1 Coating Thickness 2 Coating Thickness 3 Coating Thickness 4 Coating Thickness 5 Coating Dencity 1 Coating Dencity 2 Coating Dencity 3 Coating Dencity 4 Coating Dencity 5

Coating Data Tcoat 1 Tcoat 2 Tcoat 3 Tcoat 4 Tcoat 5 ρ coat 1 ρ coat 2 ρ coat 3 ρ coat 4 ρ coat 5

0,0003 0,0003 0,0024 0 0 1300 900 900 0 0

m m m m m kg/m3 kg/m4 kg/m5 kg/m6 kg/m7

5,00E-06 0,0625 1 0,2 18000 10000

silt and clay mm

Soil Interaction Soil clay Bottom Roughness zo Seabed Grain Size d50 Reduction Factor, Permeable Seabed τ perm,z Friction Coefficient µ Dry Unit Soil Weight Ys Underained Shear Strength Su Environmental Parameter Spectral Spreading exponent Reference Curret Height Water Depth Peak Enhancement Factor Storm Duration Safety Class Factor Wave and Current Data 1 Year Hs (Tinggi Significant) 12 Tp(s) (Periode Signivicant) 12 Uc (s) (Kecepatan significant) 0,4

99 3 100 3,3 3 10 year 14 15 0,5

N/m3 N/m3

m m hours 100 year 15 18 0,6

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 : T n=



√ √

d 100 = =3.19 s g 9.81

Peak Wave Frequency : ωp =

2 π 2 x 3.14 = =0.42 rad /s Tp 15

; T p =15 s

Note : wave and current data for 10 years period 

The Generalised Philips’ constant is given by : γ 1−0.287 . ln ¿ 2 4 5 H s ωp 5 142 x 0.42 4 (¿¿)= ( 1−0.287 ln3.3 ) =0.01 6 g2 6 9.812 α =¿

(



)

The spectral width parameter is given by : 0.07 if ω ≤ ω p σ= 0.09 else

{

σ =0.09(ω> ω p )

ω= 

2 π 2 x 3.14 = =1.97 Tn 3.19

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

G2 ( ω )=



ω 1.97 = =1.82 sinh( kd) sinh(0.54 x 100)

For the JONSWAP spectrum, which is often appropriate, the spectral density function reads :

[ ( )]

exp −0.5

−4

( ( )) −5 ω 4 ωp

.γ

ω−ω p σ . ωp

2

¿ S ηη ( ω )=α . g2 . ω−5 .exp ¿ −5

−4

( ( ))

−5 1.97 S ηη ( ω )=0.01 x 9.81 x 1.97 exp 4 0.42 2

x 3.3

[ (

exp −0.5

1.97−0.42 0.09 x0.42

)] 2

S ηη ( ω )=0.04 

The wave induced velocity spectrum at the sea bed S UU (ω) may be obtained through a spectral transformation of the waves at sea level using a first order wave theory : S uu ( ω )=G 2 (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=∫ ω n SUU (ω)dω 0

because we use order 0, so the value of the spectral moments is M 0=S ηη ( ω )

M 0=0.14 We use order 2 to compare the spectral moments : ∞

M n=∫ ω n SUU ( ω ) dω 0

2

2

M 2=ω x SUU =1.97 x 0.14=0.54 

Therefore, the significant flow velociy amplitude at pipe level is : U s =2 √ M 0 U s =2 √0.04=0.75 m/s



Mean zero up-crossing period of oscillating flow at pipe level is : T u =2 π

τ=

√

√

M0 0.04 =2 x 3.14 =3.19 s M2 0.54

T 15 = =4.7 T u 3.19

LOADS CALCULATION 

The ratio between the design single oscillation velocity amplitude and the design spectral velocity amplitude for kU =

1 2

(√ 2 ln τ + 0.5772 √ 2 ln τ )

kU =

1 2

(√ 2 ln 4.7+ √0.5772 2 ln 4.7 )

k U =1.04 ¿

kU =

U Us

τ

oscillations :



Oscillatory velocity amplitude for single design oscillation, perpendicular to pipeline defined as : ¿ U =k U x U s=1.04 x 0.75=0.78



Steady current velocity associated with design oscillation, perpendicular to pipeline given by : ln ( z + z 0 ) −ln z 0 V ¿ =V .( zr ). . sin θ c ln ( z r + z 0 ) −ln z 0 ¿

V =0.5 x 3 x

ln [ 100+ ( 5 x 10−6 )−ln(5 x 10−6 ) ] ln [ 3+ ( 5 x 10 )−ln(5 x 10 ) ] −6

−6

sin 90°

V ¿ =1.90 m/ s 

Period associated with single design oscillation T ¿ =T u=3.19 s



Keulegan-Carpenter number for single design oscillation : ¿ ¿ U x T 0.78 x 3.19 K ¿= = =7.20 D 0.3445



Steady to oscillatory velocity ratio for design : V ¿ 1.90 M ¿= ¿ = =2.44 U 0.78



Cy

is get from table 3-9 “Peak Horizontal Load Coefficient” (DNV RP F109

page 25)

So, 

Cz

C y =1.5

is get from table 3-9 “Peak Horizontal Load Coefficient” (DNV RP F109

page 25)

Rasio antara design oscillation velocity amplitude dan design spectral velocity amplitude untuk osilasi kU =

U¿ 1 = Us 2

τ

adalah :

(√ 2 ln τ + 0.5772 √ 2 ln τ )

C y =1.03

So,

Peak horizontal and vertical load are : 1 2 F¿Y =r tot , y . . ρw . D . C¿Y . ( U ¿ +V ¿ ) 2 1 ¿ 2 FY =1 . .1025 . 0,3415 .1,5 . ( 0,78+1,9 ) =1875,85 2

N/m

1 2 F¿z=r tot, y . . ρw . D . C¿z . ( U ¿ +V ¿ ) 2 1 ¿ 2 FY =1 . .1025 . 0,3415 .1,03 . ( 0,78+1,9 ) =1288,08 2 

N/m

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

[

W s=

( F D+ F I )+ μ . F L μ

]

max

. Fw

using this formula to find the value of drag force, lift force and inertia force : Lift Force : 1 F L = . ρ w . C L D ( U s . cos θ+U C )2 2

; CL = 0.9

1 F L = x 1.025 x 0.9 x 0.3445 x 0.74 2 2 F L =4.40 N Drag force : 1 F D = . ρ w . C D D|( U s . cos θ+U C )|( U s cos θ+U c ) ; C = 0.7 D 2 1 F D = x 1025 x 0.7 x 0.3445|( 0.74 )|( 0.74 ) 2 F D =3.42 N

Inertia Force : F I=

π D2 ρ C A sin θ 4 w m s

; CM = 3.29

where As=

2 π U s 2 x 3.14 x 0.74 = =1.46 Tu 3.19

So the inertia force is : 2

F I=

3.14 x 0.3445 x 1025 x 3.29 x 1.46 sin 90° 4

F I =40.18 N

Therefore the submerged weight is:

[

F D+ FI + μ FL μ

[

3.42 x 40.18 x 0.2 x 4.40 x1 0.2

W s=

W s=

]

max

. Fw

]

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) Gc =

Su D. γ s

Gc =

10.000 0,3445 .18.000

Gc =1,61 Fc =W S −F z Fc =2322,38−1298,81 Fc =1023,57 N γ ' sc =13500

K c=

Su. D Fc

; clay (very dense)

K c=

10000 .0,3445 1023,57

K c =3,37

F R=

1023,57 . 4,1 .3,37 0,39 1,61

F R=11722, 85 N

Criteria : ¿

¿

F + μ+ F Z γ SC . γ ≤1 μ . wS + F R

1,83.

1891,48+0,2+1298,81 ≤1 0,2 .2322,38+11722,85

0,31 ≤1

Vertical Stability γw

b ≤1 w s +b

1,1

936,79 ≤1 2322,38+936,79

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

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