1.Input

1.1 Pipeline Design Parameter.

Outer diameter• Ds 12in:= Corrosion coating density• ρcorr 940kg m3−

⋅:=

Wall thickness• ts 12.7mm:= Concrete coat density• ρcc 3044kg m3−

⋅:=

Internal diameter• ID Ds 2ts−( ):= Content density• ρcont 10kg m3−

⋅:=

Corrosion coating thickness• tcorr 3mm:= Seawater density• ρsw 1025kg m3−

⋅:=

Pipe joint length• L 12.2m:= Steel density• ρs 7850kg m3−

⋅:=

Concrete coating thickness assumption• tcc 0mm 0 in⋅=:=

1.2 Environmental Parameter

Water depth• d 70m:=

Kinematic viscosity of seawater• v 1.076 105−

⋅ ft2

sec1−

⋅:=

1.2.1 Installation Condition (1 year return period data)

Significant Wave Height• Hs.i 1.2m:=

Spectral peak period• Tp.i 15sec:=

Significant Wave period• Ts.i

Tp.i

1.05:=

Ts.i 14.286 s=

Current at 90% depth• Ur.i 0.165m sec1−

⋅:=

1.2.2 Operation Condition (100 year return period data)

Significant Wave Height• Hs.o 2.5m:=

Spectral peak period• Tp.o 11sec:=

Significant Wave period• Ts.o

Tp.o

1.05:=

Ts.o 10.476 s=

Current at 90% depth• Ur.o 0.33m sec1−

⋅:=

Corrosion allowance• ca 3mm:=

Marine growth thickness• tmg 51mm:=

Marine growth density• ρmg 1400kg m3−

⋅:=

1.3 Soil Parameter

Soil type • 1 = sand

2 = claysoil 2:=

Medium density of sand• ρsand 1860kg m3−

⋅:=

Medium density of clay• ρclay 326.309kg m3−

⋅:=

Medium density of soil• ρsoil ρsand soil 1=if

ρclay soil 2=if

:= ρsoil 326.309kg

m3

=

Undrained shear stress• Su 2kPa:=

Medium density of clay• ρclay 326.309kg m3−

⋅:=

2. Calculation

2.1 Vertical Stability

2.1.1 Instalation condition

Internal diameter IDi Ds 2ts−( ):= IDi 0.279m=

Total outer diameter Dtot.i Ds 2 tcorr⋅+ 2 tcc⋅+( ):= Dtot.i 0.311m=

Corrosion coating diameter Dcorr Ds 2 tcorr⋅+( ):= Dcorr 0.311m=

Steel pipe mass / length Wst.iπ

4Ds2

IDi2

−

⋅ ρs⋅:= Wst.i 91.486

kg

m=

Corrosion coating mass / length Wcorrπ

4Dcorr

2Ds2

−

⋅ ρcorr⋅:= Wcorr 2.727

kg

m=

Concrete coat mass / length Wcc.iπ

4Dtot.i

2Dcorr

2−

⋅ ρcc⋅:= Wcc.i 0

kg

m=

Content mass / length Wcont.iπ

4IDi

2⋅ 0⋅:= Wcont.i 0=

Buoyancy Bcc.iπ

4Dtot.i

2ρsw⋅:= Bcc.i 77.763

kg

m=

Total mass / length Wtot.i Wst.i Wcorr+ Wcc.i+ Wcont.i+ Bcc.i−:= Wtot.i 16.449kg

m=

VERTICAL STABILITY SGcc.i

Wtot.i Bcc.i+( )Bcc.i

:= SGcc.i 1.212=

VSi "OK!" SGcc.i 1.1>if

"Enlarge concrete coating thickness" SGcc.i 1.1≤if

:=VSi "OK!"=

2.1.2 Operation condition

Internal diameter IDo Ds 2 ts ca−( )⋅− := IDo 0.285m=

Corrosion coating diameter Dcorr Ds 2 tcorr⋅+:= Dcorr 0.311m=

Concrete coating diameter Dcc.o Dcorr 2 tcc⋅+:= Dcc.o 0.311m=

Total outer diameter Dtot.o Ds 2 tcorr⋅+ 2 tcc⋅+ 2.tmg+( ):= Dtot.o 0.413m=

Steel pipe mass / length Wst.oπ

4Ds2

IDo2

−

⋅ ρs⋅:= Wst.o 70.593

kg

m=

Corrosion coating mass / length Wcorrπ

4Dcorr

2Ds2

−

⋅ ρcorr⋅:= Wcorr 2.727

kg

m=

Concrete coat mass / length Wcc.oπ

4Dcc.o

2Dcorr

2−

⋅ ρcc⋅:= Wcc.o 0

kg

m=

Marine growth mass / length Wmgπ

4Dtot.o

2Dcc.o

2−

⋅ ρmg⋅:= Wmg 81.155

kg

m=

Content mass / length Wcont.oπ

4IDo

2⋅ ρsw⋅:= Wcont.o 65.572

kg

m=

Buoyancy Bcc.oπ

4Dtot.o

2ρsw⋅:= Bcc.o 137.181

kg

m=

Total mass / length Wtot.o Wst.o Wcorr+ Wcc.o+ Wmg+ Wcont.o+ Bcc.o−:= Wtot.o 82.867kg

m=

VERTICAL STABILITY SGcc.o

Wtot.o Bcc.o+( )Bcc.o

:= SGcc.o 1.604=

VSo "OK!" SGcc.o 1.1>if

"Enlarge concrete coating thickness" SGcc.o 1.1≤if

:=VSo "OK!"=

2.2 Lateral Stability

2.2.1 Instalation Condition

2.2.1.1 Water Particle Velocity Calculation Caused by Wave Induced Velocity

Periode referensi Tnd

g:= Tn 2.672 s=

Peakedness parameterϕi

Tp.i

Hs.i

:= ϕi 13.693s

m0.5

=

γi 5 ϕi 3.6sec

m≤if

1 ϕi 5sec

m≥if

3.3 otherwise

:= γi 1=

Figure 2.1 Significant water velocity, Us

* (DNV RP E305)

Water particle velocity

(Wave induced)

Tn

Tp.i

0.178=

Us.i

0.23 Hs.i⋅

Tn

:= Us.i 0.103m

s=

Figure 2.2 Zero-up crossing period, Tu (DNV RP E305)

Zero-up crossing period Tu.i 0.985 Tp.i⋅:= Tu.i 14.775 s=

2.2.1.2 Average Velocity on Pipeline

Velocity on 90% depth Ur.i 0.165m

s=

Besarnya arus yang melewati pipa dipengaruhi oleh jenis tanah seabed dimana p ipa diletakkan.

dalam hal tanah merupakan tanah clay, maka kekasaran tanah diabaikan, sehingga UD.i = Ur.i

UD.i Ur.i 0.165m

s=:=

2.2.1.3 Simplified Static Stability Method

Wave particle acceleration As.i 2 π⋅Us.i

Tu.i

⋅:= As.i 0.044m

s2

=

Ki

Us.i Tu.i⋅

Dtot.i

:= Ki 4.911=Keilegan-Carpenter number

Wave - current velocity ratio Mi

UD.i

Us.i

:= Mi 1.597=

2.2.1.3.1 Hydrodynamics coefficient

Reynold's number Rei

UD.i Us.i+( )v

Dtot.i⋅:= Rei 8.342 104

×=

Drag coefficient CD.i 1.2 Rei 3 105

⋅< Mi 0.8≥∧if

0.7 otherwise

:= CD.i 1.2=

Lift coefficient CL 0.9:=

Inertia coefficient CM 3.29:=

2.2.1.3.2 Calibration Factor

Figure 5.12 Calibration factor, Fw, as function of K and M (DNV RP E305)

Calibration factor Fw.i 1:=

2.2.1.3.3 Seabed Soil Factor

Figure 5.11 Recommended friction factors for clay (DNV RP E305)

ratioi

Dtot.i Su⋅

Wtot.i g⋅:= ratioi 3.853=

Soil friction factor μi 0.25:=

2.2.1.4 Lateral Stability Calculation

Hydrodynamic forces and Required submerged weight

i 0 180..:=phase angle range

θi

i deg⋅:=

FL.i. θ( )1

2

ρsw

g⋅ Dtot.i⋅ CL⋅ Us.i cos θ( )⋅ UD.i+( )2⋅:=

Lift force

Drag force FD.i. θ( )1

2

ρsw

g⋅ Dtot.i⋅ CD.i⋅ Us.i cos θ( )⋅ UD.i+( )2⋅:=

Inertia force FI.i. θ( ) πDtot.i

2

4⋅

ρsw

g⋅ CM⋅ As.i⋅ sin θ( )⋅:=

Required submerged weight Ws.i. θ( )FD.i. θ( ) FI.i. θ( )+( ) μi FL.i. θ( )⋅+

μi

Fw.i⋅:=

Wreq.i. θ( ) max Ws.i. θ( )( ):=

Wreq.i. θ( ) 8.488kg

m=

SFw.i

Wtot.i

Wreq.i. θ( ):= SFw.i 1.938=

LSi "OK!" SFw.i 1≥if

"Enlarge concrete coating thickness" SFw.i 1<if

:= LSi "OK!"=LATERAL STABILITY

2.2.2 Operation Condition

2.2.2.1 Water Particle Velocity Calculation Caused by Wave Induced Velocity

Periode referensi Tnd

g:= Tn 2.672 s=

Peakedness parameterϕo

Tp.o

Hs.o

:= ϕo 6.957s

m0.5

=

γo 5 ϕo 3.6sec

m≤if

1 ϕo 5sec

m≥if

3.3 otherwise

:= γo 1=

Figure 2.1 Significant water velocity, Us

* (DNV RP E305)

Water particle velocity

(Wave induced)

Tn

Tp.o

0.243=

Us.o

0.12 Hs.o⋅

Tn

:= Us.o 0.112m

s=

Figure 2.2 Zero-up crossing period, Tu (DNV RP E305)

Zero-up crossing period Tu.o 1.08 Tp.o⋅:= Tu.o 11.88 s=

2.2.2.2 Average Velocity on Pipeline

Velocity on 90% depth Ur.o 0.33m

s=

Besarnya arus yang melewati pipa dipengaruhi oleh jenis tanah seabed dimana p ipa diletakkan.

dalam hal tanah merupakan tanah clay, maka kekasaran tanah diabaikan, sehingga UD.i = Ur.i

UD.o Ur.o 0.33m

s=:=

2.2.2.3 Simplified Static Stability Method

Wave particle acceleration As.o 2 π⋅Us.o

Tu.o

⋅:= As.o 0.059m

s2

=

Ko

Us.o Tu.o⋅

Dtot.o

:= Ko 3.232=Keilegan-Carpenter number

Wave - current velocity ratio Mo

UD.o

Us.o

:= Mo 2.939=

2.2.2.3.1 Hydrodynamics coefficient

Reynold's number Reo

UD.o Us.o+( )v

Dtot.o⋅:= Reo 1.826 105

×=

Drag coefficient CD.o 1.2 Reo 3 105

⋅< Mo 0.8≥∧if

0.7 otherwise

:= CD.o 1.2=

Lift coefficient CL 0.9:=

Inertia coefficient CM 3.29:=

2.2.2.3.2 Calibration Factor

Figure 5.12 Calibration factor, Fw, as function of K and M (DNV RP E305)

Calibration factor Fw 1:=

2.2.2.3.3 Seabed Soil Factor

Figure 5.11 Recommended friction factors for clay (DNV RP E305)

ratioo

Dtot.o Su⋅

Wtot.o g⋅:= ratioo 1.016=

Soil friction factor μo 1.3:=

2.2.2.4 Lateral Stability Calculation

Hydrodynamic forces and Required submerged weight

i 0 180..:=phase angle range

θi

i deg⋅:=

FL.o. θ( )1

2

ρsw

g⋅ Dtot.o⋅ CL⋅ Us.o cos θ( )⋅ UD.o+( )2⋅:=

Lift force

Drag force FD.o. θ( )1

2

ρsw

g⋅ Dtot.o⋅ CD.o⋅ Us.o cos θ( )⋅ UD.o+( )2⋅:=

Inertia force FI.o. θ( ) πDtot.o

2

4⋅

ρsw

g⋅ CM⋅ As.o⋅ sin θ( )⋅:=

Required submerged weight Ws.o. θ( )FD.o. θ( ) FI.o. θ( )+( ) μo FL.o. θ( )⋅+

μo

Fw⋅:=

Wreq.o. θ( ) max Ws.o. θ( )( ):=

Wreq.o. θ( ) 8.231kg

m=

SFw.o

Wtot.o

Wreq.o. θ( ):= SFw.o 10.068=

LSo "OK!" SFw.o 1≥if

"Enlarge concrete coating thickness" SFw.o 1<if

:= LSo "OK!"=LATERAL STABILITY

Dapat dilihat pada bagian 1. Input, bahwa tebal concrete coating yang dimasukkan adalah tcc = 0 mm.

Pada perhitungan kestabilan vertikal, dapat dilihat nilai SG yang lebih dari 1, maka pipa dinyatakan stabil baik dalam kondisi instalasi

maupun operasi.

Pada perhitungan kestabilan lateral, dapat dilihat nilai SF yang lebih dari 1, maka pipa dinyatakan stabil baik dalam kondisi instalasi

maupun operasi.

Pernyataan kestabilan pipa dalam arah vertikal dan lateral tersebut diperoleh dalam kondisi tebal concrete coating = 0 mm, maka

disimpulkan bahwa pipa tidak memerlukan conrete coating. hal tersebut diperoleh dengan mengiterasi beberapa nilai tebal concrete

coating, hingga diambil kesimpulan tersebut di atas.