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INTRODUCTION This calciulation sheet presents the wall thickness analysis of a single walled flowline installed on the seabed. The wall thickness calculations are carried out, based on allowable stress design code PD 8010 (Ref. 1), for the following load scenarios: 1. Reeling (if applicable); 2. Pressure containment (bursting); 3. Local buckling (collapse); 4. Propagation buckling. The hydrostatic strength and leak test pressure values are also determined. This calculation sheet also assesses the selected wall thickness for Von Mises Equivalent stress for when the pipeline is over a prop (vertical upset).

REFERENCES 1. Code of Practice for Pipeline -Part 2: Subsea Pipelines.British Standard PD 8010, July 2004. 2. Specification for Line Pipe.API Specification 5L, October 2010. 3. Submarine Pipeline Systems.DNV OS-F101, October 2010.

ASSUMPTIONS 1. Code of Practice for Pipeline -Part 2: Subsea Pipelines.British Standard PD 8010, July 2004. 2. Specification for Line Pipe.API Specification 5L, October 2010. 3. Submarine Pipeline Systems.DNV OS-F101, October 2010.

UNITS DEFINITIONS

Enter only data highlighted.Other data have already been defined below.

Temperature

C 1 K * :

g 9.81 m * s 2 -^* :

Gravity

1. INPUT DATA

1.1 Pipeline Data

Pipe outer diameter:

D.o 168.3 mm * :

Pipe Young's modulus:

E 207103^* MPa * :

ρ.st 7850 kg * m 3 -^* :

Pipe material density:

Pipe specified minimum yield strength:

SMYS 550 MPa * :

Pipe design temperature: (enter value in Centigrade Celsius)

T.d 75 C * :

Specify material type:

Material CMn :

CMn is for carbon manganese (carbon steel ); DSS is for 22Cr duplex and 25Cr super duplex

Bend thinning

B 10 % * :

Pipe corrosion allowance:

t.corr 0 mm * :

Pipe overall coating thickness:

t.coat 0 mm * :

Pipe total ovality when installed: (includes manufacturing & bending, e.g. reeling)

f.o 2.5 % * :

User's tolerance input (if different from above):

ntol 10 % * :

Poisson's ratio:

ν 0.3 :

α 1.3 105 -^* C 1 -^* :

Pipe's coefficient of thermal expansion:

1.2 Pipe Content Data

Internal design pressure (gauge):

P.d 100 bar * :

Enter level height where design pressure is specified:

ρ.i 1025 kg * m 3 -^* :

Density of operational contents:

1.3 Environmental Data

Min & Max water depth:

depth.min 34.1 m * :

depth.max 34.1 m * :

h.ref 0 m * :

Reference height above water level (if not known set to zero):

ρ.sw 1025 kg * m 3 -^* :

Density of seawater:

Seawater temperature: (enter value in Centigrade Celsius)

T.sea 4 C * :

1.4 Vessel Data

Reeling condition: Select Yes or No, whether the pipe is installed by reel method (e.g. Seven Navica) or otherwise.

Vessel reel radius: (e.g. Seven Navica)

R.reel 7.5 m * :

Bottom residual horizontal tension after pipeline installation: (if not known set to zero)

T.bot 0 kN * :

1.5 Design Factors

Note: The user does not need to alter the load factors defined below.

Design factor for Hoop stress (see Table 2, Section 6.4.1,Ref. 1)

f.d_hoop 0.72 :

Design factor for Equivalent stresses resulting from functional and environmental or accidental loads (see Table 2, Section 6.4.1,Ref. 1)

f.d_func 0.96 :

Subsea 7 strain factor for reeling:

f.strain 0.67 :

2. CALCULATIONS

2.1 Initial Calculations

Material yield derating due to elevated temperature is done in accordance to DNVGL-ST-F101 the material SMYS is derated in this Mathcad sheet.Derating for carbon steel (C-Mn) pipe and duplex stainless steel (DSS) pipe (22Cr & 25Cr) (see Figure 2, Section 5-C304, Ref. 3)

Carbon steel (CMn) derating

stress_derating 00307041 mat 106^* Pa * :

temperature 05010020041 mat C * :

stress_derate.CMn temperature C / stress_derating Pa / T.d C / linterp Pa * :

stress_derate.CMn MPa 15

Duplex stain steel (DSS) derating

stress_derating 00409012014061 mat 106^* Pa * :

temperature 0205010015020061 mat C * :

stress_derate.DSS temperature C / stress_derating Pa / T.d C / linterp Pa * :

stress_derate.DSS MPa 65

Yield strength derating at design temperature:

σ.y SMYS stress_derate.CMn - :

σ.y MPa 535

P.i P.d :

Assumed internal pressure at seabed

External pressure at seabed (for min & max WD)

P.o_min ρ.sw g * depth.min * :

P.o_max ρ.sw g * depth.max * :

P.o_max Pa 3.4288 105^*

P.o_min Pa 3.4288 105^*

Allowable Hoop stress

σ.A_h f.d_hoop σ.y * :

Allowable equivalent stress

σ.A_e f.d_func σ.y * :

Temperature difference

ΔT T.d T.sea - :

2.2 Reeling Criteria -Local Buckling -Bending During Reeling (see Annex G, Ref. 1) Note: The calculation of the minimum reelable wall thickness is only applicable for a pipe bent around a curvature on a vessel duringinstallation (e.g. reeled pipe).If this is not the case, the value of reelable wall thickness is set to zero (see condition below).

ε.b D.o 2 R.reel D.o 2 / + t.coat + (* / :

ε.b 0.0111

Functional strain from bending (pipe strain when bent around a radius)

Characteristic bending strain for buckling due to bending moments acting alone (See eq. G.8, Annex G-Section G.1.4, Ref. 1)

Find minimum reelable wall thickness Note:The minimum reelable wall thickness is found by equating the functional strain from bending to the characteristic bending strain for buckling due to bending moments acting alone (expressions given above).

Assign an initial value to the thickness to enable solution to converge

t.reel ε.b 15 t D.o / (2^* f.strain * ≡ t 5.5866 mm * ≡ FindRoot :

Minimum nominal reelable wall thickness

t.reel mm 5.5866

Note:The wall thickness determined above is the nominal wall thickness and therefore the fabrication tolerance is understood to be included (see notation of wall thickness in eq. G.8, Section G.1.4, Ref. 1, and definition in Section 3.2, Ref. 1). The nominal wall thickness is also defined is Section 6.4.2.2.Also the corrosion allowance needs not be taken into into account (see definition) since this operation of reeling the pipe is temporary and is in air.

2.3 Pressure Containment (Internal Pressure) (see Section 6.4.2.2, Ref. 1)

Note: If water depth varies, use min value to calculate the hydrostatic pressure Po (the use of max value of depth yields unconservative wall thickness value). Note: There are 2 formulations that are used to determine the required wall thickness to withstand burst, thin wall and thick wall theories.The application of either theory is governed by the OD/tmin ratio.

Thin wall theory (see Section 6.4.2.2, Ref. 1)

Assign an initial value to wall thickness to enable solution to converge

t.thin mm 2.1846

t.thin σ.A_h P.i (D.o 2 t.m * / * ≡ t.m 2 mm * ≡ FindRoot :

t.thin σ.A_h P.i (D.o 2 t.m * / * ≡ t.m 2 mm * ≡ FindRoot eval :

Thick wall theory (see Section 6.4.2.2, Ref. 1)

Assign an initial value to wall thickness to enable solution to converge

t.thick σ.A_h P.i (D.o 2^D.o 2 t.t * - (2^+ D.o 2^D.o 2 t.t * - (2^- / * ≡ t.t 1 mm * ≡ FindRoot :

t.thick mm 2.1569

Indicate correct wall theory based on diameter/wall ratio

t.min D.o t.thin / 20 > t.thin t.thick if 11 line :

Determine nominal wall thickness for internal pressure criteria based on correct wall D/t

t.min 0.0022 m *

Nominal wall thickness for internal pressure criteria Note: The corrosion allowance and fabrication tolerance are not included in the above value and therefore need to be taken into account.

t.int_press t.min 1 ntol - (/ t.corr + (:

t.int_press mm 2.4273

t.bends t.min 1 ntol - (/ t.corr + (11 B - (/ * :

t.bends mm 2.697

2.4 Local Buckling -External Pressure (Hydrostatic Collapse) (see Annex G-Section G.1.2, Ref. 1) Note: Use maximum water depth for external hydrostatic pressure.

t.nom P.e 2 E 1 ν 2^- / * t.nom D.o / (3^* :

Critical external pressure (see eq. G.2, Annex G-Section G.1.2, Ref. 1)

t.nom P.y 2 σ.y * t.nom D.o / * :

Yield pressure (see eq. G.3, Annex G-Section G.1.2, Ref. 1)

Collapse pressure (Based on maximum water depth)

P.c P.o_max :

Assign an initial t.nom value to wall thickness to enable solution to converge, play around with to get the most logical solution

t.hydro_coll P.c t.nom P.e / 1 - (P.c t.nom P.y / (2^1 - (* P.c t.nom P.y / f.o D.o t.nom / * (* ≡ t.nom 2 mm * ≡ FindRoot :

t.hydro_coll mm 1.581

2.5 Propagation Buckling (see Annex G-Section G.2, Ref. 1) Use maximum water depth for external hydrostatic pressure.

Assign an initial t.n value to wall thickness to enable solution to converge, play around with the value get the most logical solution

t.prop_buck P.o_max 10.7 σ.y * t.n D.o / (2.25^* ≡ t.n 5 mm * ≡ FindRoot :

t.prop_buck mm 2.2355

3. SELECTED API WALL THICKNESS

Reeling Criterion

t.reel #

Pressure containment (internal pressure - burst)

t.int_press mm 2.4273

t.bends mm 2.697

Local buckling (external pressure -collapse)

t.hydro_coll mm #

Propagation buckling -installation (pipe empty)

t.prop_buck mm #

Selected standard nominal wall thickness:

t.API 11.00 mm * :

t.b 11.00 mm * :

Wall Thickness Calculation