85342161 OBS Installation Airy

Seabed Steady Current Velocity•

d 23.38 m=d do LAT−:=Water depth final (-LAT)•

LAT 0.62m:=LAT•

do 24m:=Water depth•

Tp2 7.176 sec=Tp2250Hs

g:=Tp 6.048 sec=Tp 1.05 Ts⋅:=Spectral peak period•

Ts 5.76 sec⋅:=Significant wave period•

Should be in meterHs 2.02m:=

CM 3.29:=Inertia Coeff.•

CL 0.9:=Lift Coeff.•

1.2.1 HYDRODYNAMIC COEFFICIENT

φcurr 90deg:=Angle between current direction and pipeline direction•

φwave 90deg:=Angle between wave direction and pipeline direction•

ν 1.076 10 5−⋅ ft2 sec 1−

:=Kinematic Viscosity of Seawater•

ρsw 64 pcf⋅:=Seawater density•

Zr 2.338 m=Zr 10% d⋅:=Ur 0.44m sec 1−⋅:=

ρcorr 59pcf:=Density corr. coating• Outer Diameter• Ds 30in:=

1.1.2 DENSITY1.1.1 PIPELINE PARAMETER

1.1 PIPELINE DESIGN PARAMETER

Equivalent conditionPhase : InstallationWave/Current Data : 1 yr return period wave + 1 yr return period currentSoil Type : Medium Sand

pcf lb ft 3−⋅:=

1. INPUT PARAMETER

ZONE 2 (24-47m)

The objective of this spreadsheet is to perform analysis on the On-Bottom Stability in accordance to Airy Wave Method, DNV 1981 & DnV RP E305

OBJECTIVE:

ON-BOTTOM STABILITY CALCULATION

Significant Wave Height•

1.2 ENVIRONMENTAL PARAMETER

ρs 490 pcf⋅:=Steel density•Thermal Insulation coating thickness• tins 0in:=

ρcont 0 pcf⋅:=Content density•Corrosion coating thickness (3LPE)• tcorr 2.5mm:=

ρcc 190 pcf⋅:=Concrete coat. Density•Internal Diameter• ID Ds 2ts−:=

ρins 0 pcf⋅:=Thermal insulation coat. Density•Wall thickness• ts 0.752in:=

OBS Installation Tugas Besar S2_Z2.mcd 1 of 4

D tcc( ) 33.397 in= includes concrete coating

Internal Diameter: Di Ds 2 ts⋅−:= Di 28.496 in=

Dcorr Ds 2tcorr+:=

Dins Dcorr 2tins+:=

Submerged Weight = Steel Weight + Corrosion Coat Weight + Thermal Insulation + Jacket material + Concrete Coat Weight + Contents Weight - Buoyancy

Ws tcc( ) π

4Ds

2 ID2−⎛

⎝⎞⎠ ρs⋅ Dcorr

2 Ds2

−⎛⎝

⎞⎠ ρcorr⋅+ Dins

2 Dcorr2

−⎛⎝

⎞⎠ ρins⋅+

D tcc( )2 Dins2

−⎛⎝

⎞⎠ ρcc ID2

ρcont⋅+ D tcc( )2 ρsw⋅−+

...⎡⎢⎢⎣

⎤⎥⎥⎦

:=

Ws tcc( ) 60.492lbft

=

Bouyancy B tcc( ) π

4D tcc( )2ρsw:= B tcc( ) 389.33

lbft

=

2.2 VERTICAL STABILITY

SvWs tcc( ) B tcc( )+

B tcc( ):= Sv 1.1≥ Sv 1.155=

if Sv 1.1≤ "need more thickness", "OK",( ) "OK"=

1.3 SOIL PARAMETER

Soil type 1 = sand, 2 = clay soil 1:=

1.3.1 FRICTION COEFFICIENT 1.3.2 SAFETY FACTOR

Clay soil: Sand Soil:Fs 1.1:=

µc 0.3:= µs 0.7:=

µ µs soil 1=if

µc otherwise

:= µ 0.7=

2. CALCULATIONS

2.1 SUBMERGED WEIGHT CALC.This section calculate provided weight by pipeline section

Total Outer Diameter: D tcc( ) Ds 2tcorr+ 2 tins⋅+ 2tcc+:= D tcc( ) 33.397 in=

Total Outside Diameter:


dL d( )

0.414=L d( ) Find L( ):=

λ L d,( ) L=

Given

intermediate depth approximation

deep approximation

shallow approximationλ L d,( ) Tp g d⋅dL

125

<if

g Tp2

⋅

2 π⋅

dL

12

>if

g Tp2

⋅

2 π⋅tanh

2 π⋅ d⋅L

⎛⎜⎝

⎞⎠

⋅ otherwise

:=Wave Length

Calculation of Wave Length (cont.)

L 187.305 ft=Lg Tp

2⋅

2 π⋅:=Initial Guess

Calculation of Wave Length

This section calculates the wave induced velocity and acceleration for a given phase angle. The phase angle is calculated for the worst case on-bottom pipeline stability.

2.3 WAVE INDUCED VELOCITY CALC.


Aw d θ,( )Hs π⋅

Tp

gd

dL d( )

125

<if

2Hsπ

Tp

⎛⎜⎝

⎞

⎠

2⋅ e

k d( ) D tcc( )( ) d−⎡⎣ ⎤⎦⋅ dL d( )

12

>if

Hsg π⋅

L d( )

cosh k d( ) D tcc( )( )⋅⎡⎣ ⎤⎦cosh k d( ) d⋅( )

⋅ otherwise

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

sin θ( )⋅:= shallow approximation

deep approximation


Aw max Aw d θ,( )( ):=

Significant wave acceleration perpendicular to pipe Aw d θ,( ) Aw Rwave⋅:= Aw d θ,( ) 0.536ft

sec2=

Reynold's Number Re tcc( )

Uw d θ,( ) Ur+( )D tcc( )ν

:= Re tcc( ) 5.068 105×=

M Number MUr

Uw d θ,( ):= M 2.799= Remember if K>50 & M>=0.8, Fw=1.2

Force Coefficient

CD 1.2 Re tcc( ) 3 105⋅< M 0.8≥∧if

0.7 otherwise

:= CD 0.7=

Horizontal Water Particle Velocity

k d( )2 π⋅

L d( ):=

Phase angle range:i 0 90..:= θ i i deg⋅:=

u d θ,( )Hs2

gd

dL d( )

125

<if

π Hs⋅

Tpek d( ) D tcc( ) d−( )⋅ d

L d( )12

>if

Hs2

g Tp⋅

L d( )

cosh k d( ) D tcc( )( )⋅⎡⎣ ⎤⎦cosh k d( ) d⋅( )

⋅ otherwise

⎡⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎦

cos θ( )⋅:= shallow approximation

deep approximation


uw max u d θ,( )( ):= uw 0.516ft

sec=

Reduction factor due to wave directionality Rwave sin φwave( ):= Rwave 1=

Significant wave velocity perpendicular to pipe Uw d θ,( ) uw Rwave⋅:= Uw d θ,( ) 0.516ft

sec=

Horizontal Water Particle Acceleration


Inertia Force: FI θ tcc,( )π D tcc( )2⋅

4

ρswg

⋅ CM⋅ Aw d θ,( )⋅ sin θ( )⋅:=

Required Submerged Weight: Ws θ tcc,( )FD θ tcc,( ) FI θ tcc,( )+( ) Fs⋅ µ FL θ tcc,( )⋅+

µ

⎡⎢⎣

⎤⎥⎦

:=

2.6 RESULT OF CALCULATION

0 10 20 30 40 50 60 70 80 9020

30

40

50

60Submerged Weight Vs Phase Angle

Phase Angle (deg)

Subm

erge

d W

eigh

t (lb

/ft)

Change the concere thickness until its okConcrete thickness

tcc 1.6in≡

109mm 4.291 in=

Wreq max Ws θ tcc,( )( ):=

Ws tcc( ) 60.492lbft

= Wreq 54.767lbft

=

if Ws tcc( ) Wreq≤ "need more thickness", "OK",( ) "OK"=

Safety factor for submerged weight due to requirement weight SFwWs tcc( )

Wreq:= SFw 1.105=

Submerged Weight Ws tcc( ) 60.492lbft

=

2.4 STEADY CURRENT VELOCITY CALC.

Ratio of effective velocity to reference current velocity Ueff Ur:=

Reduction factor due to current directionality Rcurr sin φcurr( ):= Rcurr 1=

Significant wave velocity perpendicular to pipe Uc_eff Ueff Rcurr⋅:= Uc_eff 1.444ft

sec=

2.5 LATERAL STABILITY CALCULATION

Hydrodynamic forces and Required Submerged Weight

Phase angle range: i 0 90..:= θ i i deg⋅:=

Lift Force: FL θ tcc,( ) 12

ρswg

⋅ D tcc( )⋅ CL⋅ Uw d θ,( ) Uc_eff+( )2⋅:=

Drag Force: FD θ tcc,( ) 12

ρswg

⋅ D tcc( )⋅ CD⋅ Uw d θ,( ) Uc_eff+( )2⋅:=


85342161 OBS Installation Airy

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