Free Span- As Lay- 12 Inch-Production(KP0-KP6.5) No Lock Function
-
Upload
icemage1991 -
Category
Documents
-
view
64 -
download
12
description
Transcript of Free Span- As Lay- 12 Inch-Production(KP0-KP6.5) No Lock Function
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
SU TU NAU PROJECT-DNV RP-F105 FREE SPANNING PIPELINE
Project_info"SU TU NAU FIELD DEVELOPMENT"
"As-Laid Case "
Pipeline_Description "12inch Production Pipeline from STN-N (KP0) to STN-S (KP6.55)"
1.0 INTRODUCTION
This Mathcad sheet has been written in order to calculate in-line and cross flow vortex induced vibration onset and screening lengths of pipelines in accordance withDNV-RPF105Free Spanning Pipelines 2006 (Reference [1]). The sheet calculates the following span limits:VIV onsetFatigue screeningULS criterion (according to Reference [2]) considering both static and dynamic loadingOn-bottom wave and current velocities are calculated using methodology contained within both Reference [1] and Reference [2]. The sheet is set up to perform calculations onan untrenched pipeline configuration. Screening data is always 1 year return period wave data, and 100 year return period current data.Onset lengths can be based upon 1, 10 or 100 year data depending upon the loadcase under consideration. ULS check should consider 100 year current for operatingconditions, and 10 year for temporary conditions, it is a project decision whether maximum wave height and period should be used. Cyclonic conditions will require carefulevaluation of overall velocities and dissemination of these into suitable wave and current components.Sheet performs calculations for the length of the pipeline route of the above for the as-laid, flooded, hydrotest and operating loadcases.For VIV calculations, operating pressures and temperatures are used.Half of any corrosion allowance should be considered - Guidance Note in Section 2.2.5 Reference [1]. NOTE THAT THIS MAY VARY ON A PROJECT BASIS.Corrosion not considered for calculation of effective axial force [and hence frequencies, onset and screening lengths] but is included for stress calculations - Section 6.2.2Reference [1].For ULS criterion check, corrosion allowance is conservatively EXCLUDED when calculating pipeline loading, but INCLUDED when considering pipeline capacity.For ULS criterion check, MAXIMUM wave height and associated period is considered for static loading. Dynamic loading uses SIGNIFICANT values. Design temperaturesand pressures are used.Simplified soils damping criteria are used for this calculationIt is currently assumed that functional loading does not reduced the combined loading effect, refer to Note 1 of Table 4-4 Reference [2].Sheet is set up for single, non-interacting spans only - interacting spans require FE Analysis to determine natural frequencies.Sheet assumes pipe is fully restrained. If this is not the case, an effective axial force may require to be manually input for the operational loadcase.References1. Det Norske Veritas, DNV-RP-F105 - Free Spanning Pipelines, 2006.2. Det Norske Veritas, DNV-OS-F101 - Submarine Pipeline Systems, 20123. Det Norske Veritas, DNV-RP-F109 - On-bottom Stability Design of Submarine Pipelines, 2007.4. Det Norske Veritas, DNV-GL-14 - Free Spanning Pipelines, 1998.5. Det Norske Veritas, DNV-RP-C205 - Environmental Conditions and Environmental Loads April 2010
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 1/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
General Functions / Unit Definition
Find largest value in a column of a matrixmax_find matrix col( ) match max matrix
col matrixcol
0
Matrix trim function trim_rows matrix max_rows( ) submatrix matrix 0 max_rows 0 cols matrix( ) 1 return
0 2Listbox state saving functions Effective Axial Force Pipe Roughness
1 2Equation to use for Seff Span Definition
0 2Loadcase Duration Span Boundary Conditions
val_find val vec( ) lst_vec last vec( )
0 0 return val vec0if
lst_vec lst_vec( )return val veclst_vecif
if val vecii= ii ii 1 ii return val veciiif
ii 1 lst_vecfor otherwise
Value finder - finds the relative position of a value in a vectorof values in terms of which values it lies between.
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 2/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
2D Linear Interpolation linear_interp X Y XYs Xs Ys( ) y_min y_max( ) val_find Y Ys( )
x_min x_max( ) val_find X Xs( )
xvalsXsx_min
Xsx_max
yvalsYsy_min
Ysy_max
x_inter x yv( ) linterp xvalsXYsx_min yv
XYsx_max yv
X
y_inter xv y( ) linterp yvalsXYsxv y_min
XYsxv y_max
Y
XYsx_min y_minreturn x_min x_max=if
x_inter X y_min( )return otherwise
y_min y_max=if
y_inter x_min Y( )return x_min x_max=if
linterp xvalsy_inter x_min Y( )
y_inter x_max Y( )
X
return otherwise
otherwise
3D Linear Interpolation multi_interp X Y Z XYss Xs Ys Zs( ) z_min z_max( ) val_find Z Zs( )
zvalsZsz_min
Zsz_max
xy_1 linear_interp X Y XYssz_min Xs Ys
xy_2 linear_interp X Y XYssz_max Xs Ys
xy_1return z_min z_max=if
linterp zvalsxy_1
xy_2
Z
return otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 3/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Modified Parameter Interpolation for Gc G_param_inter M N table( ) mvals table0
m_min m_max( ) val_find M mvals( )
n_min n_max( ) val_find N0.003
0.006
min_offset ii 4 n_min 1
max_offset ii 4 n_max 1
p_1 tablem_min min_offset
p_2 tablem_min max_offset
m_min m_max=if
p_1 linterp mvals tablemin_offset
M
p_2 linterp mvals tablemax_offset
M
otherwise
rmii p_1 n_min n_max=if
rmii linterp0.003
0.006
p_1
p_2
N
otherwise
ii 0 3for
rm
Floating-Point Comparison Operators Less than fp_lt x y( ) if round x 6 round y 6 1 0
Less than or equal to fp_lte x y( ) if round x 6 round y 6 1 0
Equal to fp_eq x y( ) if round x 6 round y 6 = 1 0
Greater than or equal to fp_gte x y( ) if round x 6 round y 6 1 0
Greater than fp_gt x y( ) if round x 6 round y 6 1 0
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 4/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
General Functions / Unit Definition
2.0 INPUT SUMMARY
2.1 Pipeline Properties
Interval for calculations KPStep 100 m
2.1.1 Pipeline Mechanical Properties
pipe_inputs
Pipe Section
Start KP(km)
End KP(km)
Steel OD
D0(mm)
Steel Wall Thickness
tnom(mm)
Internal Coat
Thickness
tint(mm)
Internal Coat
Density
ρint(kg/m3)
Corrosion Allowance
tcor(mm)
Corrosion Coat
Thickness
tcc(mm)
Corrosion Coat
Density
ρcc(kg/m3)
Concretethickness
twc(mm)
ConcreteCoat
Density
ρwc(kg/m3
)
Marine Growth
Thickness
tma(mm)
Marine Growth Density
ρma(kg/m3
)1 0 6.55 323.9 9.5 0 0 3 35.3 200 55 3040 0 1500
2.1.2 Seabed Properties2.1.3 Safety Class Definition
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 5/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Seabed
KP From KP To Soil TypeSoil Type Integer for Calculations
SeabedRoughness
Associated Roughness
Poisson's Ratio
0 6.55 Medium Sand 1 Medium sand 4.00E-05 0.35
Safety
KP From KP To Safety ClassInteger forCalculation
0 6.55 Low 0
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 6/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
2.1.4 Axial Friction Coefficiens Soil Type: Table 7.3 - 7.4 Section 7.3.1 Page 35 Ref. [1]Seabed Roughness: Table 3.1, Section 3.2.6 Page 19 Ref. [1]White cells are protected, as they calculate the values required by the sheet basedon the selected drop down option.
Axial
KP From KP ToAxial Friction
Coefficient
0 6.55 0.5
2.2 Pipeline Mechanical Properties
Young's modulus of Steel E 207000 MPa Turbulence Intensity Ic 5% Section 3.2.12 Page20 Ref. [1]
Steel density ρs 7850kg m3
Poisson's Ratio of Steel ν 0.3
Field joint infill density ρfj 1025 kg m3
Percentage of Pipeline Diameterused to Calculate Min. Span Gap
e0 30%
Nominal pipe joint length Lpj 12.2m Residual Lay Tension Heff 0kN
Concrete cutback length FJ 470mm Tide and Surge Tsurge 4.09m
SMYS SMYS 450MPa Design Pressure Pdes 0bar
SMTS SMTS 535MPa Operating Pressure Poper 0bar
Young's Modulus of Concrete Ec 30242.52MPa Reference Elevation for Pressure (LAT) elev 20.19m
Linear Thermal Expansion coefficient αe 11.7 106
°C1
Structural Damping ζstr 0.01 Section 6.2.11 Page31,Ref. [1]
Hydrodynamic Damping Section 4.1.8 ζh 0 Section 4.1.9 Page 23 Ref. [1]Steel loss during Operation CA 0%
Redefinition of dimension of user input vectors - Do not modify
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 7/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Function to convert a distance to a matrix integer KP x( )
x
KPStep
Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.
Set case counter - find number of rows containing data forpipe / headings / bathy data
n_pipe max_find pipe_inputs 0 n_pipe 0.00ip 0 n_pipe
n_SF max_find Safety 0 n_SF 0.00
Trim each matrix such that they are the same size as theactual data set
pipe_inputs trim_rows pipe_inputs n_pipe( )
Safety trim_rows Safety n_SF( )
2.2.7 Pipe Section Data Allocation and Validity Checks
pipe_sec pipe_inputs0
Pipe Sections
pipe_start_kp pipe_inputs1
kmKP Start Points
KP End Points pipe_end_kp pipe_inputs2
km
Steel OD pipe_OD pipe_inputs3
mm
Steel WTtnom pipe_inputs
4 mm
Internal Coat thickness tint pipe_inputs5
mm
Internal Coating Density ρint pipe_inputs6
kg m3
Corrosion Allowance tcorr pipe_inputs7
mm
Corrosion Coating Thickness tcc pipe_inputs8
mm
Corrosion Coating Density ρcc pipe_inputs9
kg m3
Conctete Coating Thickness twc pipe_inputs10
mm
Concrete Coating Density ρwc pipe_inputs11
kg m3
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 8/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Marine Growth Thicknesstmar pipe_inputs
12 mm
Marine Growth Density ρmar pipe_inputs13
kg m3
KP_input_check kps kpe( ) result 1
result result kpsii kpeii 1=
ii 1 last kps( )for last kps( ) 0if
"Section KP points incorrectly specified"
"KP inputs OK"
result
return
General function for checking KP input validity
KP_pipe_input_check KP_input_check pipe_start_kp pipe_end_kp( )
KP_pipe_input_check "KP inputs OK"2.2.8 Pipe Properties Data Allocation and Function Definition
Index values for vectors created x_v 0 1pipe_end_kplast pipe_end_kp( )
KPStep Length of the Pipe
Length pipe_end_kplast pipe_end_kp( )KP values to run calculation for KP_vx_v x_v KPStep
Length 6550.00 m
Function to find the index of the section which contains xUsed to transform section data into functions - i.e.replaces an interpolation function to find the value of avariable at any point along the route
x_find x end_val( ) ii 0
lst_val last end_val( )
ii ii 1
ii last end_val( ) x end_valiiwhile
iireturn
pipe_find x( ) x_find x pipe_end_kp( )
Pre-allocate row indices for the pipe section properties KP_indexPIx_v
pipe_find KP_vx_v
Steel OD Do x( ) pipe_ODKP_indexPIKP x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 9/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Steel WT tnom x( ) tnomKP_indexPIKP x( )
Internal Coat thicknesstint x( ) tintKP_indexPIKP x( )
Internal Coating Density ρint x( ) ρintKP_indexPIKP x( )
Corrosion Allowance tcorr x( ) tcorrKP_indexPIKP x( )
tcc x( ) tccKP_indexPIKP x( )Corrosion Coating Thickness
ρcc x( ) ρccKP_indexPIKP x( )Corrosion Coating Density
twc x( ) twcKP_indexPIKP x( )Conctete Coating Thickness
ρwc x( ) ρwcKP_indexPIKP x( )Concrete Coating Density
Marine Growth Thicknesstmar x( ) tmarKP_indexPIKP x( )
Marine Growth Density ρmar x( ) ρmarKP_indexPIKP x( )
Safety Class
Safety_start_kp Safety0
km
Safety_end_kp Safety1
km
Safety_find x( ) x_find x Safety_end_kp( )
KP_indexSCx_v
Safety_find KP_vx_v
Safety Classsafetyclass Safety
2 safety_class x( ) safetyclassKP_indexSCKP x( )
Integer Safety Class
S_C Safety3
SC x( ) S_CKP_indexSCKP x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 10/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Seabead properties n_SB max_find Seabed 0
n_SB 0.00last Safety_end_kp( ) 0.00
Seabed trim_rows Seabed n_SB( )
sea_start_kp Seabed0
kmSafety_end_kp0 6550.00 m
sea_end_kp Seabed1
km
Seabed 0.00 6.55 "Medium Sand" 1.00 "Medix_v 0 1
sea_end_kplast sea_end_kp( )
KPStep
KP_vx_v x_v KPStep
sea_find x( ) x_find x sea_end_kp( )Seabed 0.00 6.55 "Medium Sand" 1.00 "
KP_Sea_indexSBx_v
sea_find KP_vx_v
zo Seabed5
zo x( ) zoKP_Sea_indexSBKP x( )
Soil Seabed3
Soil x( ) SoilKP_Sea_indexSBKP x( )
Poisson's Ratio υsoil Seabed6
νsoil x( ) υsoilKP_Sea_indexSBKP x( )
Remove inputs from memory pipe_inputs 0 Safety 0 Seabed 0
Redefinition of dimension of user input vectors - Do not modify
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 11/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 12/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
2.3 Operational Data
2.3.1 Water Depth 2.3.2 Trench depth 2.3.3 Internal Pressure Profiles
water_depthKP
[km]Water Depth
[m]
0 37.71
0.01 37.7
0.02 37.7
0.03 37.7
0.04 37.69
0.05 37.69
trench_depthKP
[km]Trench Depth
[m]0 0
6.55 0
OpPresKP
[km]
OperatingPressure
[bar]
Design Pressure
[bar]0 0 0
6.55 0 0
2.3.4 Temperature Profiles 2.3.5 Density Profiles 2.3.6 Empirical KC Section 6.2.5 Page 30. Ref. [1]Temp
KP
[km]
OperatingTemperature
[0C]
DesignTemperature
[0C]0.00 0.00 0.006.55 0.00 0.00
Den
KP
[km]
Contents Density- Op
[kg/m-3]
Contents Density- De
[kg/m-3]0 0 0
6.55 0 0
Emp_KCKP
[km]Empirical KC
0 0.256.55 0.25
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 13/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Effective Axial Force 2.3.7 Seawater Data 2.3.8 Manual Input - Effective Axial ForceSeffinput
Calculated (Fully Restrained)Manual Input
SaveSEFF "" 0
SWTemp
KP
[km]
Ambient Seawater
Temperature
[0C]
Density
[kg/m-3]
0 19.3 10256.55 19.3 1025
Seffman
KP
[km]
Effective Axial Force -
OPERATING[kN]
Effective AxialForce - DESIGN
[kg/m-3]
0 0 06.55 0 0
Equation to use for effective axial force
WallThick WallThin Wall Approximation (DNV OS F101)
SaveWall "" 0
Loadcase DurationLCinput
Less than 6 monthsMore than 6 months
SaveLC "" 0
Temperature FOR INSTALLATION - this is usedin order to calculate the fully restrained axial force
Pipe Properties Data Processing (No User Input Required)
n_WD max_find water_depth 0 n_WD 655.00
Water depth water_depth trim_rows water_depth n_WD( )
pipe_WD_KP water_depth0
km
pipe_WD water_depth1
m
WD x( ) linterp pipe_WD_KP pipe_WD x( )
Prseures n_OP max_find OpPres 0 n_OP 1.00
OpPres trim_rows OpPres n_OP( )
pipe_POP_KP OpPres0
kmAppendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 14/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
pop_KP OpPres1
bar
pdes_KP OpPres2
bar
Opreating Prseures Pope x( ) linterp pipe_POP_KP pop_KP x( ) Design Prseures Pde x( ) linterp pipe_POP_KP pdes_KP x( )
This value is using for ULS CheckContent Density
n_Den max_find Den 0 n_Den 1.00
Den trim_rows Den n_Den( )
pipe_Den_KP Den0
km
ρop_Den_KP Den1
kg m3
ρdes_Den_KP Den2
kg m3
Content density Ope ρop x( ) linterp pipe_Den_KP ρop_Den_KP x( ) Content density Des ρdes x( ) linterp pipe_Den_KP ρdes_Den_KP x( )
Temperature n_Tem max_find Temp 0
Temp trim_rows Temp n_Tem( )
pipe_Tem_KP Temp0
km
top_Tem_KP Temp1
°C
tde_Tem_KP Temp2
°C
Temperature Ope Top x( ) linterp pipe_Tem_KP top_Tem_KP x( ) Temperature Des TULS x( ) linterp pipe_Tem_KP tde_Tem_KP x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 15/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Seawater Temperature n_Sea max_find SWTemp 0
SWTemp trim_rows SWTemp n_Sea( )SWTemp
0.00
6.55
19.30
19.30
1025.00
1025.00
pipe_Tamb_KP SWTemp0
km
tamb_Tamb_KP SWTemp1
°Cpipe_Tamb_KP
0.00
6550.00
m
ρw_Tamb_KP SWTemp2
kg m3
Temperature of Seawater Tamb x( ) linterp pipe_Tamb_KP tamb_Tamb_KP x( ) Denity of water ρw x( ) linterp pipe_Tamb_KP ρw_Tamb_KP x( )
Prseures using for ULS Prseures Operation
pldULS x( ) Pde x( ) Pop x( ) Pope x( )
Empirical constant n_KC max_find Emp_KC 0
Emp_KC trim_rows Emp_KC n_KC( )
pipe_KC_KP Emp_KC0
km
KC Emp_KC1
Emp_KC0.00
6.55
0.25
0.25
kc x( ) linterp pipe_KC_KP KC x( )
Axial Friction n_soil max_find Axial 0 n_soil 0.00
Trim matrix such it is the same size as the actual data set Axial trim_rows Axial n_soil( ) Axial 0.00 6.55 0.50
Give each column of data a relevant name
Section Start Point soil_start Axial0
km
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 16/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Section End Point soil_end Axial1
km
soil_find x( ) x_find x soil_end( )
Pre-allocate row indices for soil data KP_indexSDx_v
soil_find KP_vx_v
Axial Friction nguyax Axial2
μax x( ) nguyaxKP_indexSDKP x( )
Manual Input - Effective Axial Forcen_Seff max_find Seffman 0
n_Seff 1.00
Seffman trim_rows Seffman n_Seff( )
pipe_Seffm_KP Seffman0
km
Seffman0.00
6.55
0.00
0.00
0.00
0.00
Seffman_onset_KP Seffman
1 kN
Seffman_uls_KP Seffman2
kN
Seffman_onset x( ) linterp pipe_Seffm_KP Seffman_onset_KP x( )
Seffman_uls x( ) linterp pipe_Seffm_KP Seffman_uls_KP x( )
Trench depth n_trench max_find trench_depth 0
trench_depth trim_rows trench_depth n_trench( )
pipe_trench_KP trench_depth0
km
depth_trench_KP trench_depth1
m
dtrench x( ) linterp pipe_trench_KP depth_trench_KP x( )
Remove inputs from memory water_depth 0 OpPres 0 SWTemp 0 Den 0 Temp 0 Emp_KC 0 Axial 0 Seffman 0
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 17/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
trench_depth 0
Pipe Properties Data Processing (No User Input Required)
2.4 Code Data - Boundary Conditions, Safety Factors from DNV RP-F105
Pipe RoughnessTable 5.1 Section 5.4.4 Page 29 Ref. [1]
Span DefinitionTable 2.3, Section 2.6.2 Page 18 Ref. [1]
Span Boundary ConditionsTable 6.1 Section 6.7.8 Page 33 Ref. [1]
roughnessSteel, PaintedSteel, uncoated (not rusted)ConcreteMarine Growth
SaveSteelRough "" 0
Span_DefVery Well Defined - Survey DataWell Defined - FE analysisNot Well Defined
SaveSpan_Def "" 0
BCPinned-PinnedFixed-FixedSingle Span on the SeabedPinned-Fixed
SaveBC "" 0
λ1 1.3 fn12 2.7Ratio between first and secondmodes of crossflow vibrationMode Shape Weighting Factor Section 5.2.7 Page 28 Ref [1] Section 6.8.1 Page 34 Ref [1]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 18/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
VIV Safety Factors Table 2.3 Section 2.6.2 Page 18 Ref [1] Screening Criteria Safety Factors Table 2.1, Section 2.6.1 Page 18γIL 1.4 γCF 1.4
γf
Low Normal HighVery well defined 1 1 1Well defined 1.05 1.1 1.15Not well defined 1.1 1.2 1.3
Free span typeSafety Class
Table 2-3 Safety factor for natural frequencies, γf
Table 2.3 Section 2.6.2, Page 18 Ref [1]
γf x c( ) γfSpan_Def SC x( ) c 0=if
1 otherwise
Safety Factors Table 2.2 Section 2.6.2, Page 18 Ref [1]
Stability parameter
η
γk
γs
γonIL
γonCF
Low Normal High
1 0.5 0.25
1 1.15 1.3
VIVULSVIVULSVIVULS
Safety ClassTable 2-2 General safety factors for fatigue
Safety Factor
η
γk
γs1.31
γon,IL
γon,CF
1.11
1.21
γk x c( ) γk0 SC x( )c 0=if
1 otherwise
For ULS criterion γf and γk are equal to 1. γk is also one for safety class low, i.e.temporary loadcases. For operational spanning, they vary as above.For screening, γf is not required, and is set to one in the calculations
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 19/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Select Appropriate Safety Factors Table 6.1 Section 6.7.8, Page 33 Ref [1]Boundary condition coefficients
Fixed-pinned values for:C1 and C2 taken from DNV GL14C3 to C6 calibrated from literature and DNV GL14
C1
1.57
3.56
3.56
2.45
C2
1.0
4.0
4.0
2.0
C3
0.8
0.2
0.4
0.5
C4 L Leff( )
4.93
14.1
max 14.1 L
Leff
2 8.6
10.2
C5 L Leff( )
1
8
1
12
max 18 Leff
L
2 6
1
1
24
1
8
C6
5
384
1
384
1
384
2
384
C1 C1BC C2 C2BC C3 C3BC
C1 3.56 C2 4.00 C3 0.40
C4 L Leff( ) C4 L Leff( )BC C5 L Leff( ) C5 L Leff( )BC C6 C6BC C6 2.6042 103
2.5 Code Data - Safety Factors from DNV OS-F101
Material Fabrication Factor αfab 1 Table 5.7, Section 5 C307 Page 45 Ref [2]
Functional Load Factor γfLC 1.1 Table 4.4, Section 4 G201Page 39 Ref [2]
Material Resistance Factor γm 1.15 Table 5.4, Section 5 C205 Page 44 Ref [2]
Environmental Load Factor γE 1.3 Table 4.4, Section 4 G201 Page39 Ref [2]
Safety Class Factor γSC 1.04 Table 5.5 Section 5 C206 Page 44 Ref [2]
Condition Load factor γc 1.07 Table 4.5, Section 4, G203,Page 40 Ref [2]
Material Strength factor αU 0.96 Table 5.6 Section 5 C306 Page 45 Ref [2]
Ovality f0 1.5% Table 7.17 Section 4 G314Page 83 Ref [2]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 20/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
2.6 Environmental Data
Sheet will calculate VIV onset lengths and ULS lengths based on the worst of the following combinations:10yr wave / 1yr current and 1yr wave / 10yr current for temporary cases.100yr wave / 10yr current and 10yr wave / 100yr current for the operating case.Should temporary cases extend beyond 6 months, then 10 year / 100 year data should be used.Note that the screening case considers long term current (10 yr for temporary cases less than 6 months, 100 yr otherwise) with 1 year wave. It is therefore suggested thatall three tables are filled in, to ensure all required data is present. If they are not all available it is conservative to e.g. consider 10year return period data for the 1year input.
RP_1year
KP From[km]
KP to[km]
Wave HightHs(m)
SpectralPeak
Period Tp[s]
Near-bottomvelocityUwd[m/s]
Mean ZeroUp-
CrossingPeriod Tu[s]
Wave /VelocityHeading
Øw(0)
Maximum Waveheight
Hmax[m]
AssociatedPeriodTmax[m]
Near-BottomVelocity
Umaxd[m/s]
Max Wave /
VelocityHeading
Ømax(0)
CurrentVelocityUc[m/s]
CurrentHeading
Øc(0)
0 6.55 3.5 7.8 90 6.94 7.13 90 0.23 90
RP_10year
KP From[km]
KP to[km]
Wave HightHs(m)
SpectralPeak
Period Tp[s]
Near-bottomvelocityUwd[m/s]
Mean ZeroUp-
CrossingPeriod Tu[s]
Wave /VelocityHeading
Øw(0)
Maximum Waveheight
Hmax[m]
AssociatedPeriodTmax[m]
Near-BottomVelocity
Umaxd[m/s]
Max Wave /
VelocityHeading
Ømax(0)
CurrentVelocityUc[m/s]
CurrentHeading
Øc(0)
0 6.55 5.5 10.6 90 10.58 9.65 90 0.53 90
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 21/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
RP_100year
KP From[km]
KP to[km]
Wave HightHs(m)
SpectralPeak
Period Tp[s]
Near-bottomvelocityUwd[m/s]
Mean ZeroUp-
CrossingPeriod Tu[s]
Wave /VelocityHeading
Øw(0)
Maximum Waveheight
Hmax[m]
AssociatedPeriodTmax[m]
Near-BottomVelocity
Umaxd[m/s]
Max Wave /
VelocityHeading
Ømax(0)
CurrentVelocityUc[m/s]
CurrentHeading
Øc(0)
0 6.55 8 14.1 90 14.78 12.79 90 0.73 90
current_data
1 year 10 year 100 year
Height at which Velocity Given zc m 1 1 1
RETURN PERIODPARAMETER VARIABLE UNITS
Data Processing (No User Input Required)
For 1 year Period
Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.
Set case counter - find number of rowscontaining data
n_RP1 max_find RP_1year 0
Trim matrix such it is the same size as the actual data set RP_1year trim_rows RP_1year n_RP1( )
KP Starts RP_start_kp1 RP_1year0
km
KP Ends RP_end_kp1 RP_1year1
km
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 22/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
KP index for spectral input table spec_find1 x( ) x_find x RP_end_kp1( )
KP_indexspec1x_v
spec_find1 KP_vx_v RP_1year 0.00 6.55 3.50 7.80 0.0
JONSWAP Spectral Parameters
JONSWAP Significant Wave Height HS_1 RP_1year2
m HS_1 x( ) HS_1KP_indexspec1KP x( )
JONSWAP Peak Wave Period Tp_1 RP_1year3
s Tp_1 x( ) Tp_1KP_indexspec1KP x( )
Near-bottom velocity Uw1_sig_input RP_1year4
m s1
Uw1sig_input x( ) Uw1_sig_inputKP_indexspec1KP x( )
Mean Zero Up-Crossing Period Tu_1_input RP_1year5
s Tu_1_input x( ) Tu_1_inputKP_indexspec1KP x( )
Max Near-bottom velocity Uw1_max_input RP_1year9
m s1
Uw1max_input x( ) Uw1_max_inputKP_indexspec1KP x( )
Angle between Wave and Pipeline Heading: θw_1_calcsig RP_1year6
deg θw_1_sig x( ) θw_1_calcsigKP_indexspec1KP x( )
Extreme Wave Parameters
Expected Max Single Wave Height Hmax_1 RP_1year7
m Hmax_1 x( ) Hmax_1KP_indexspec1KP x( )
Assoc Period of EHmax THmax1 RP_1year8
s Tmax_1 x( ) THmax1KP_indexspec1KP x( )
Angle between Wave and Pipeline Heading: θw_1_max RP_1year10
deg θw_1_max x( ) θw_1_maxKP_indexspec1KP x( )
General Current Parameters
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 23/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.
Steady Current Uc1 RP_1year11
m s1
Uc_1 x( ) Uc1KP_indexspec1KP x( )
Angle between Current andPipeline Heading:
θc1 RP_1year12
deg θc_1 x( ) θc1KP_indexspec1KP x( )
For 10 year Period
Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.
Set case counter - find number of rowscontaining data
n_RP10 max_find RP_10year 0
Trim matrix such it is the same size as the actual data set RP_10year trim_rows RP_10year n_RP10( )
KP Starts RP_start_kp10 RP_10year0
km
KP Ends RP_end_kp10 RP_10year1
km
KP index for spectral input table spec_find10 x( ) x_find x RP_end_kp10( )
KP_indexspec10x_v
spec_find10 KP_vx_v
JONSWAP Spectral Parameters
JONSWAP Significant Wave Height HS_10 RP_10year2
m HS_10 x( ) HS_10KP_indexspec10KP x( )
JONSWAP Peak Wave Period Tp_10 RP_10year3
s Tp_10 x( ) Tp_10KP_indexspec10KP x( )
Angle between Wave and Pipeline Heading: θw_10_calcsig RP_10year6
deg θw_10_sig x( ) θw_10_calcsigKP_indexspec10KP x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 24/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Near-bottom velocity Uw10_sig_input RP_10year4
m s1
Uw10sig_input x( ) Uw10_sig_inputKP_indexspec10KP x( )
Mean Zero Up-Crossing Period Tu_10_input RP_10year5
s Tu_10_input x( ) Tu_10_inputKP_indexspec10KP x( )
Max Near-bottom velocity Uw10_max_input RP_10year9
m s1
Uw10max_input x( ) Uw10_max_inputKP_indexspec10KP x( )
Extreme Wave Parameters
Expected Max Single Wave Height Hmax_10 RP_10year7
m Hmax_10 x( ) Hmax_10KP_indexspec10KP x( )
Assoc Period of EHmax THmax10 RP_10year8
s Tmax_10 x( ) THmax10KP_indexspec10KP x( )
Angle between Wave and Pipeline Heading: θw_10_max RP_10year10
deg θw_10_max x( ) θw_10_maxKP_indexspec10KP x( )
General Current Parameters
Steady Current Uc10 RP_10year11
m s1
Uc_10 x( ) Uc10KP_indexspec10KP x( )
Angle between Current andPipeline Heading:
θc10 RP_10year12
deg θc_10 x( ) θc10KP_indexspec10KP x( )
For 100 year Period
Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.
Set case counter - find number of rowscontaining data
n_RP100 max_find RP_100year 0
Trim matrix such it is the same size as the actual data set RP_100year trim_rows RP_100year n_RP100( )
KP Starts RP_start_kp100 RP_100year0
km
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 25/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
KP Ends RP_end_kp100 RP_100year1
km
KP index for spectral input table spec_find100 x( ) x_find x RP_end_kp100( )
KP_indexspec100x_v
spec_find100 KP_vx_v
JONSWAP Spectral Parameters
JONSWAP Significant Wave Height HS_100 RP_100year2
m HS_100 x( ) HS_100KP_indexspec100KP x( )
JONSWAP Peak Wave Period Tp_100 RP_100year3
s Tp_100 x( ) Tp_100KP_indexspec100KP x( )
Angle between Wave and Pipeline Heading: θw_100_calcsig RP_100year6
deg θw_100_sig x( ) θw_100_calcsigKP_indexspec100KP x( )
Near-bottom velocity Uw100_sig_input RP_100year4
m s1
Uw100sig_input x( ) Uw100_sig_inputKP_indexspec100KP x( )
Mean Zero Up-Crossing Period Tu_100_input RP_100year5
s Tu_100_input x( ) Tu_100_inputKP_indexspec100KP x( )
Max Near-bottom velocity Uw100_max_input RP_100year9
m s1
Uw100max_input x( ) Uw100_max_inputKP_indexspec100KP x( )
Extreme Wave Parameters
Expected Max Single Wave Height Hmax_100 RP_100year7
m Hmax_100 x( ) Hmax_100KP_indexspec100KP x( )
Assoc Period of EHmax THmax100 RP_100year8
s Tmax_100 x( ) THmax100KP_indexspec100KP x( )
Angle between Wave and Pipeline Heading: θw_100_max RP_100year10
deg θw_100_max x( ) θw_100_maxKP_indexspec100KP x( )
General Current Parameters
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 26/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Steady Current Uc100 RP_100year11
m s1
Uc_100 x( ) Uc100KP_indexspec100KP x( )
Angle between Current andPipeline Heading:
θc100 RP_100year12
deg θc_100 x( ) θc100KP_indexspec100KP x( )
Height at which Velocity Given
Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.
Set case counter - find number of rowscontaining data
n_curr100 max_find current_data 0 n_curr100 0.00
Trim matrix such it is the same size as the actual data set current_data trim_rows current_data n_curr100( ) current_data 1.00 1.00 1.00
Reference Height (for waves/ currents) zr_c_1 current_data( )0 0 zr_c_1 1.00
zr_c_10 current_data0 1 zr_c_10 1.00
zr_c_100 current_data0 2 zr_c_100 1.00
Remove inputs from memory current_data 0 RP_100year 0 RP_10year 0 RP_1year 0
Data Processing (No User Input Required)
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 27/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
3.0 INITIAL CALCULATIONSIntial Calculation
3.1 Backgound Values for Calculations
L 5m Translate distance used in functions to equivalent integer value KP x( )x
KPStepGuess value for span length
z 0 1 Length
KPStep Two environmental conditions are considered.
This integer is used to store the values for the pair.Integer for calculation points y 0 1
kpz z KPStep Holds the vectors for operating (VIV) and design (ULS) values c 0 1
3.2 Submerged Weight Calculation
Wall thickness t2 x( ) tnom x( ) CA tcorr x( ) Inside Diameter Di x( ) Do x( ) 2 tnom x( ) tint x( ) Used for ULS checks
Total Diameter Dt x( ) Do x( ) 2 tcc x( ) 2 twc x( ) 2 tmar x( ) Concrete Diameter Dc x( ) Do x( ) 2 tcc x( ) 2 twc x( )
Concrete diameter is used for flow velocity calculations - velocities are calculated at the pipe centreline,which will not be moved relative to the seabed by the addition of marine growth.Steel Inner Diameter Dsi x( ) Di x( ) 2 tint x( )
Second Moment of areaOf Steel
lsz
πDo kpz 4 Dsi kpz 4
64 Second Moment of area
Of Concretelconc x( ) π
Dc x( )4
Dc x( ) 2 twc x( ) 4
64
Area of steel As x( )π
4Do x( )
2Dsi x( )
2
Weight of steel Ws x( ) As x( ) ρs g Lpj
Ai x( )π
4Di x( )
2Internal Cross Section Area Weight of Contents Wc x c( ) ρc x( ) ρop x( ) c 0=if
ρdes x( ) c 1=if
Wc Ai x( ) ρc x( ) g Lpj
Wc
Wic x( )π
4Dsi x( )
2Di x( )
2
ρint x( ) g LpjWeight of Internal Coating
Weight of Field Joint Wfj x( )π
4Dc x( )
2Do x( ) 2 tcc x( ) 2
ρfj g 2 FJ
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 28/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Weight of Corrsion Coat Wcc x( )π
4Do x( ) 2 tcc x( ) 2 Do x( )
2
ρcc x( ) g Lpj
Buoyancy per metre Fb x( )π
4Dt x( )
2 ρw x( ) g Buoyancy per joint FBuoy x( ) Fb x( ) Lpj
Weight of Concrete Coating Wwc x( )π
4Dc x( )
2Do x( ) 2 tcc x( ) 2
ρwc x( ) g Lpj 2 FJ
Weight of Marine Growth Wm x( )π
4Dt x( )
2Dc x( )
2
ρmar x( ) g Lpj
Span Gap e0 x( ) e0 Dc x( )
Submerged Weight(passed into a vector) Wsub x c( )
Wc x c( ) Ws x( ) Wcc x( ) Wm x( ) Wwc x( ) Wic x( ) Wfj x( ) FBuoy x( )
Lpj
Wsubz c
Wsub kpz c
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 29/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 60
20
40
60
80
37.2
37.4
37.6
37.8
Normal Wall ThicknessAnti-corrosion Coating ThicknessConcrete Coating ThicknessInternal Coating ThinknessCorrosion AllowanceWater Depth
Wall Thickness
Distance Along Pipeline (km)
Thic
knes
s (m
m)
Wat
er D
epth
(m)
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 30/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 61
0.5
0
0.5
1
37.2
37.4
37.6
37.8
Operating PressureDesign PressureWater Depth
Pressure Profile
Distance Along Pipeline (km)
Pres
sure
(bar
g)
Wat
er D
epth
(m)
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 31/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 60
5
10
15
20
37.2
37.4
37.6
37.8
Operating TemperatureDesign TemperatureAmbient TemperatureWater Depth
Temperature Profile
Distance Along Pipeline (km)
Tem
pera
ture
(°C)
Wat
er D
epth
(m)
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 32/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 6987
987.417
987.833
988.25
988.667
989.083
989.5
Submerged Weight (VIV)Submerged Weight (ULS)
Submerged Weight
Distance Along Pipeline (km)
Subm
erge
d W
eigh
t (k
N)
3.3 Required ValuesSection 6.2.5 Page 30 Ref. [1]
Concrete Stiffness Enhancement Factor CSF x( ) kc x( )Ec lconc x( )
E lsKP x( )
0.75
Effective Mass me Ca x c( )
WsubKP x( ) c
Fb x( )
gCa
π
4 Dt x( ) 2 ρw x( )
Pcr L x( )
1 CSF x( ) C2 π2
E lsKP x( )
L2
Section 1.14.1 Page 11 Ref. [1]Critical Buckling Load
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 33/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Leff L K x( ) L
β logK 30 Do x( ) 4
1 CSF x( ) E lsKP x( )
L 30 Do x( )if
logK L
4
1 CSF x( ) E lsKP x( )
L 30 Do x( )if
4.73
0.066 β2 1.02β 0.63
β 2.7if
4.73
0.036β2 0.61β 0.63
β 2.7if
BC 2=if
1 BC 2if
Section 6.7.9 Page 33 Ref. [1]Function for Effective Span Length
Euler (Bar) buckling length limit Eulerlimit K x Seff( ) 200 Do x( ) Pop x( ) 0=if
root Pcr Leff L K x( ) x( ) Seff L otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 34/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
3.4 Effective Axial Force
μaxz
μax kpz Axial Friction
Sfr x c( ) Pi x( ) Pop x( )
ΔT x c( ) max 0 °C Top x( ) Tamb x( ) c 0=if
max 0 °C TULS x( ) Tamb x( ) c 1=if
Seff Heff 1 2 ν Pi x( )π
4 Di x( )
2 αe ΔT x c( ) E As x( ) Seffinput 0= Wall 1=if
Heff Pi x( )π
4 Di x( )
2 2 Pi x( ) ν
As x( )
4
Dsi x( )
tnom x( )1
αe ΔT x c( ) E As x( ) Seffinput 0= Wall 0=if
Seffman_onset x( ) c 0=if
Seffman_uls x( ) otherwise
Seffinput 1=if
Seffreturn
Limiter to ensure no negativetemperature assumed for temporarycases
Section 6.4.3 Page 31 Ref. [1]
Return a vector for fully restrainedforce along the line
Sfrz c
Sfr kpz c
Pipeline Section from KP 0 to KP 2.18
z1 0 1 round2180m
KPStep
Total Friction Force available from left hand end εlH1z1 c
if z1 0 μaxz1
Wsubz1 c
KPStep εlH1
z1 1 c 0
Total Friction Force available from right hand endεrH1
c
εfCy if y round2180m
KPStep
= 0 μaxy
Wsuby c
KPStep εfCy 1
y round2180m
KPStep
round2180m
KPStep
1 0for
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 35/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Fff1z1 c
max εlH1z1 c
εrH1z1 c
Pipeline Section from KP 2.18 to KP 4.36
z2 round2180m
KPStep
round2180m
KPStep
1 round4360m
KPStep
Total Friction Force available from left hand end εlH2z2 c
if z2 round2180m
KPStep
μaxz2
Wsubz2 c
KPStep εlH2
z2 1 c 0
Total Friction Force available from right hand endεrH2
c
εfCy if y round4360m
KPStep
= 0 μaxy
Wsuby c
KPStep εfCy 1
y round4360m
KPStep
round4360m
KPStep
1 round2180m
KPStep
for
Fff2z2 c
max εlH2z2 c
εrH2z2 c
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 36/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Pipeline Section from KP 4.36 to KP 6.55z3 round
4360m
KPStep
round4360m
KPStep
16550m
KPStep
Total Friction Force available from left hand end εlH3z3 c
if z3 round4360m
KPStep
μaxz3
Wsubz3 c
KPStep εlH3
z3 1 c 0
Total Friction Force available from right hand endεrH3
c
εfCy if y round6550m
KPStep
= 0 μaxy
Wsuby c
KPStep εfCy 1
y round6550m
KPStep
round6550m
KPStep
1 round4360m
KPStep
for
Fff3z3 c
max εlH3z3 c
εrH3z3 c
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 37/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Total Friction Force Fff
z cFff1
z c0 z round
2180m
KPStep
if
Fff2z c
round2180m
KPStep
z round4360m
KPStep
if
Fff3z c
otherwise
Effective axial force is the lesser of friction force or full restraint force. Seffz c
max Fffz c
Sfrz c
0 2 4 61
0.5
0
0.5
1
Fully Restrained Effective Axial ForceActual Effective Axial Force
Effective axial force
Effective axial force (kN)
Pres
sure
(bar
g)
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 38/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
WDt x( ) WD x( ) TsurgeTotal Water depth
Pe x( ) WDt x( ) g ρw x( )External Pressure
Pipe Surface Roughness kpipe x( ) kp 0.005m tmar x( ) 0mmif
kpipe m otherwise
kp
Intial Calculation
4.0 Metocean Calculations 4.1 Wave Spectra
Wave Induced Velocities - Heights and Periods
4.1.1 JONSWAP Spectrum
Angular Spectral Peak Frequency ωp Tp( )2 π
Tp JONSWAP Peak
Enhancement Factorχunit Hs Tp( )
Tp
Hs
m0.5
sec Section 3.3
Peak Enhancement Factor γ Hs Tp( ) if χunit Hs Tp( ) 3.6 5 if 3.6 χunit Hs Tp( ) 5 e5.75 1.15 χunit Hs Tp( )
1
Section 3.3.3 Page 20 Ref. [1]
Generalised Phillips' Constant αp Hs Tp( )5
16
Hs2
ωp Tp( )4
g2
1 0.287 ln γ Hs Tp( )( ) Section 3.3.3 Page 20 Ref. [1]
Spectral Width Parameter sigma ω Tp( ) if ω ωp Tp( ) 0.07 0.09
Wave Number Start value k 1 m1
k ω x( ) root k WD x( )ω
2WD x( )
gcoth k WD x( )( ) k
Section 3.3.5
Frequency Transfer Function G ω x( )ω cosh k ω x( ) Dc x( ) e0 x( )
sinh k ω x( ) WD x( )( )k ω x( ) WD x( ) 707if
0 otherwise
Section 3.3.5 Page 21 Ref. [1]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 39/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Spectral Density Function Sηη ω Hs Tp( ) αp Hs Tp( ) g2
ω5
e
5
4ω
ωp Tp( )
4
γ Hs Tp( )e
0.5ω ωp Tp( )
sigma ω Tp( ) ωp Tp( )
2
Section 3.3.3
Wave induced velocity spectrum SUU ω Hs Tp x( ) G ω x( )2
Sηη ω Hs Tp( ) Section 3.3.5
Spectral MomentsSection 3.3.6 Page 21 Ref. [1] M0 Hs Tp x( )
0s1
∞ s1
ωSUU ω Hs Tp x( )
d M2 Hs Tp x( )
0s1
∞ s1
ωSUU ω Hs Tp x( ) ω2
d
Significant Flow Velocity atPipe Centreline Us Hs Tp x( ) 2 M0 Hs Tp x( ) Section 3.3.6 Page 21 Ref. [1]
Zero Up Crossing Period Tu Hs Tp x( ) 2 πM0 Hs Tp x( )
M2 Hs Tp x( ) Section 3.4.4 Page 21 Ref. [1]
Wave energy spreading function kw s( )1π
Γ 1 s
2
Γ1
2s
2
w β s( ) kw s( ) cos β( )s
βπ
2if
0 otherwise
Wave directionality and spreading reduction factor for each wave direction
Section 3.4.3 Page 21 Ref. [1]RD θw x RD 0
rdπ
2
π
2βw β s( ) sin θw β 2
d
RD rd rd RDif
s 2 3 8for
1 Year significant wave velocity Uw1_sig_calc x( ) RD θw_1_sig x( ) x Us HS_1 x( ) Tp_1 x( ) x
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 40/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
1 Year significant wave velocityTu_1_sig x( ) Tu HS_1 x( ) Tp_1 x( ) x
10 Year significant wave velocityUw10_sig_calc x( ) RD θw_10_sig x( ) x Us HS_10 x( ) Tp_10 x( ) x
10 Year zero up-crossing period Tu_10_sig x( ) Tu HS_10 x( ) Tp_10 x( ) x
100 Year significant wave velocity Uw100_sig_calc x( ) RD θw_100_sig x( ) x Us HS_100 x( ) Tp_100 x( ) x
100 Year zero up-crossing period Tu_100_sig x( ) Tu HS_100 x( ) Tp_100 x( ) x
4.2 Short term wave conditions - Linear Wave Theory
Wave length λ Tmax x( ) rootg
2π λtanh
2π WD x( )
λ
1
2
Tmax λ 1m 1000m
Section 3.2.2.3, Page 25 Ref. [5]Wave Number k Tmax x( )
2π
λ Tmax x( )
Maximum Wave Induced Water ParticleVelocity - calculated at the top of pipe. Uwmax Hmax Tmax x( ) 0m s
1
π Hmax
Tmax
cosh k Tmax x( ) Dt x( ) sinh k Tmax x( ) WD x( )( )[ ]on error Table 3-1 Section 3.5.2.6, Page 32 Ref. [5]
1 Year maximum wave velocity Uw1_max_calc x( ) RD θw_1_max x( ) x Uwmax Hmax_1 x( ) Tmax_1 x( ) x
10 Year maximum wave velocity Uw10_max_calc x( ) RD . θw_10_max x( ) x Uwmax Hmax_10 x( ) Tmax_10 x( ) x
100 Year maximum wave velocity Uw100_max_calc x( ) RD θw_100_max x( ) x Uwmax Hmax_100 x( ) Tmax_100 x( ) x
Wave Induced Velocities - Heights and Periods
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 41/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Wave - Induced Velocities - Input at Given Reference Height
4.3 Wave-Induced Velocity Directional Calculation
Collapse this section if wave heights and periods are input. It is not required, and nor are the results used.
Significant Wave Velocity Maximum Wave Velocity
1 Year Uw1_sig_dir x( ) RD θw_1_sig x( ) x Uw1sig_input x( ) Uw1_max_dir x( ) RD θw_1_max x( ) x Uw1max_input x( )
10 Year Uw10_sig_dir x( ) RD θw_10_sig x( ) x Uw10sig_input x( ) Uw10_max_dir x( ) RD θw_10_max x( ) x Uw10max_input x( )
100 Year Uw100_sig_dir x( ) RD θw_100_sig x( ) x Uw100sig_input x( ) Uw100_max_dir x( ) RD θw_100_max x( ) x Uw100max_input x( )
Significant Wave Velocity Zero Up-Crossing Period
1 Year Uw_1z
Uw1_sig_dir z KPStep( ) HS_1 z KPStep( ) 0=if
Uw1_sig_calc z KPStep( ) otherwise
Tu_1z
Tu_1_sig z KPStep( ) Tu_1_input z KPStep( ) 0=if
Tu_1_input z KPStep( ) otherwise
10 Year Uw_10z
Uw10_sig_dir z KPStep( ) HS_10 z KPStep( ) 0=if
Uw10_sig_calc z KPStep( ) otherwise
Tu_10z
Tu_10_sig z KPStep( ) Tu_10_input z KPStep( ) 0=if
Tu_10_input z KPStep( ) otherwise
100 Year Uw_100z
Uw100_sig_dir z KPStep( ) HS_100 z KPStep( ) 0=if
Uw100_sig_calc z KPStep( ) otherwise
Tu_100z
Tu_100_sig z KPStep( ) Tu_100_input z KPStep( ) 0=if
Tu_100_input z KPStep( ) otherwise
Maximum Wave Velocity
1 Year Uw_max_1z
Uw1_max_dir z KPStep( ) Hmax_1 z KPStep( ) 0=if
Uw1_max_calc z KPStep( ) otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 42/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
10 Year Uw_max_10z
Uw10_max_dir z KPStep( ) Hmax_10 z KPStep( ) 0=if
Uw10_max_calc z KPStep( ) otherwise
100 Year Uw_max_100z
Uw100_max_dir z KPStep( ) Hmax_100 z KPStep( ) 0=if
Uw100_max_calc z KPStep( ) otherwise
Wave - Induced Velocities - Input at Given Reference Height
Current Velocities
4.4 Current Velocity Directional Calculation
Reduction Factor Rc θc sin θc Elevation aboveseabed
zed x( )e0 x( ) 0.5 Dc x( )
m Section 3.4.1 Page 21 Ref. [1]
For current in the inner zone, assuming logarithmic profile - refer to Section 3.2.6 Page 19 Ref. [1]
Average current velocity across the pipeassuming a total pipe diameter Dt :
Uc U θc zr x Rc θc Uln zed x( )( ) ln zo x( )
ln zr ln zo x( ) Section 3.2.6 Page 19 Ref. [1]
1 Year Current Uc_1z
Uc Uc_1 z KPStep( ) θc_1 z KPStep( ) zr_c_1 z KPStep
10 Year Current Uc_10z
Uc Uc_10 z KPStep( ) θc_10 z KPStep( ) zr_c_10 z KPStep
100 Year Current Uc_100z
Uc Uc_100 z KPStep( ) θc_100 z KPStep( ) zr_c_100 z KPStep
Current Velocities
5.0 SOIL PARAMETERS
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 43/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Soil Calculation
5.1 Definition of Dynamic and Static Soil Stiffnesses
Crossflow added mass coefficient
CV0
CL0
KV0
CV CL KV,S
(kN/m5/2) (kN/m5/2) (kN/m/m)Loose 10500 9000 250Medium 14500 12500 530Dense 21000 18000 1350Very Soft 600 500 50 - 100Soft 1400 1200 160 - 260Firm 3000 2600 500 - 800Stiff 4500 3900 1000 - 1600Very Stiff 11000 9500 2000 - 3000Hard 12000 10500 2600 - 4200
Sand
Clay
Table 7-5 and Table 7-6 Dynamic stiffness factor and static stiffness for pipe-soil interaction in sand and clay.
Soil Type
Section 4.5.1 Page 27 Ref. [1]
CoeffCFRES
2
2.5
8
8.5
10
1
5.5
0
0.5
0.5
KvSTAT x( ) KVSoil x( )
kN m2
CaCF Vrxf( ) linterp CoeffCFRES0
CoeffCFRES1
Vrxf
5.2 Modal Damping Ratios NB Simplified soils damping criteria is used for this calculation
soil x( ) if Soil x( ) 2 Soil x( ) if Soil x( ) 4 3 if 4 Soil x( ) 6 4 if 6 Soil x( ) 8 5 "error" Create correct soil type reference integer
L/D Ratio - to reduce sizeof below matrices
R L x( )L
Dt x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 44/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Table 7-3 Modal soil damping ratios (in %) for sand.
L/D L/D<40 100 >160 <40 100 >160
Loose 3.0 2.0 1.0 2.0 1.4 0.8Medium 1.5 1.5 1.5 1.2 1.0 0.8Dense 1.5 1.5 1.5 1.2 1.0 0.8
Horizontal (in-line) direction
Vertical (cross-flow) directionType
Table 7-4 Modal soil damping ratios (in %) for clay.
L/D L/D<40 100 >160 <40 100 >160
Very Soft - Soft 4.0 2.0 1.0 3.0 2.0 1.0Firm - Stiff 2.0 1.4 0.8 1.2 1.0 0.8Very Stiff - Hard 1.4 1.0 0.6 0.7 0.6 0.5
Horizontal (in-line) direction
Vertical (cross-flow) directionClay Type
The values given in Table 7-3 and Table 7-4 above are interpolated below to give accurate soil damping values
ζs.in L x c( )
if R L x( ) 40 3 if R L x( ) 160 1 3R L x( ) 40
60
1.5
1.5
if R L x( ) 40 4 if R L x( ) 160 1 4R L x( ) 40
60
if R L x( ) 40 2 if R L x( ) 160 0.8 2R L x( ) 40
100
if R L x( ) 40 1.4 if R L x( ) 160 0.6 1.4R L x( ) 40
150
%ζs.xf L x c( )
if R L x( ) 40 2 if R L x( ) 160 0.8 2R L x( ) 40
100
if R L x( ) 40 1.2 if R L x( ) 160 0.8 1.2R L x( ) 40
300
if R L x( ) 40 1.2 if R L x( ) 160 0.8 1.2R L x( ) 40
300
if R L x( ) 40 3 if R L x( ) 160 1 3R L x( ) 40
60
if R L x( ) 40 1.2 if R L x( ) 160 0.8 1.2R L x( ) 40
300
if R L x( ) 40 0.7 if R L x( ) 160 0.5 0.7R L x( ) 40
600
%
Total damping ratiosSection 4.1.9 Page 23 Ref. [1]
Inline ζT.inline L x c( ) ζstr ζs.in L x c( )soil x( )
ζh
Crossflow ζT.xflow L x c( ) ζstr ζs.xf L x c( )soil x( )
ζh
Soil Calculation
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 45/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
6.0 ONSET SPAN LENGTHS
6.1 Onset Reduced Velocities
Current flow ratio - Section 4.1.7
ααtz
Uc_10z
Uc_10z
Uw_1z
ααo
z
Uc_100z
Uc_100z
Uw_1z
Temporary Screening Operating Screening
Screening Current : wave ratio Guidance Note, Section 2.3.1, Page 15 Ref. [1]
Screening Current Ucscrz
Uc_10z
LCinput 0=if
Uc_100z
otherwise
ααscrz
ααtz
LCinput 0=if
ααoz
otherwise
Temporary Onset Operating Onset
Check both 10yr wave / 1yr current and 1yr wave / 10yr current Check both 100yr wave / 10yr current and 10yr wave / 100yr current
ααoiaz
Uc_1z
Uc_1z
Uw_10z
ααoib
z
Uc_10z
Uc_10z
Uw_1z
ααoa
z
Uc_10z
Uc_10z
Uw_100z
ααob
z
Uc_100z
Uc_100z
Uw_10z
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 46/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Selection of correct wave and current velocities, along with current:wave ratio.
Wave induced velocities Current velocities Current : wave ratio
Uwonsetz y
Uw_10z
y 0=if
Uw_1z
y 1=if
LCinput 0=if
Uw_100z
y 0=if
Uw_10z
y 1=if
LCinput 1=if
Uconsetz y
Uc_1z
y 0=if
Uc_10z
y 1=if
LCinput 0=if
Uc_10z
y 0=if
Uc_100z
y 1=if
LCinput 1=if
ααonz y
ααoiaz
y 0=if
ααoibz
y 1=if
LCinput 0=if
ααoaz
y 0=if
ααobz
y 1=if
LCinput 1=if
1 year / 10 year data ifduration less than 6 months
10 year / 100 year data ifduration longer than 6 months
Buoyancy ratio ρsratio x c( )
WsubKP x( ) c
Fb x( )
Fb x( ) Inline Added Mass Coefficient Ca x( ) 0.68
1.6
1 5e0 x( )
Dt x( )
e0 x( )
Dt x( )0.8if
1 otherwise
Section 6.9.1 Page 34 Ref. [1]
Also Section 3.2.15 Page 20 Ref. [1]
6.2 Reduced Velocities
Inline Stability Parameter Cross-Flow Onset Vibration Reduced Velocity
Section 4.4.6 Page 26 Ref. [1]Ksin L x c( )
4π me Ca x( ) x c ζT.inline L x c( )
ρw x( ) Dt x( ) 2 γk x c( )
ψproxi x( )1
54 1.25
e0 x( )
Dt x( )
e0 x( )
Dt x( )0.8if
1 otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 47/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
In-line Onset Vibration Reduced Velocity Section 4.3.5 Page 24 Ref. [1] Section 4.4.7 Page 26 Ref. [1]
VRILon L x c( )1.0
γonILc
Ksin L x c( ) 0.4if
0.6 Ksin L x c( )
γonILc
0.4 Ksin L x c( ) 1.6if
2.2γonIL
c
otherwise
ΔID x( ) dD min1.25 dtrench x( ) e0 x( )
Do x( )1
dtrench x( ) 0mif
dD 0 dtrench x( ) 0mif
ψtrench x( ) 1 0.5 ΔID x( )
VRCFon x c( )3 ψproxi x( ) ψtrench x( )
γonCFc
Crossflow Stability Parameter Section 4.1.8 Page 23 Ref. [1]
Kscf L x c( )4π me CaCF VRCFon x c( ) x c ζT.xflow L x c( )
ρw x( ) Dt x( ) 2 γk x c( )
Section 7.4.10 Page 37 Ref. [1]Modified Soil Stiffnesses
Inline KIL x c( ) CLSoil x( )
kN m2.5
1 νsoil x( ) 2
3ρsratio x c( )
1
3
Dt x( ) Crossflow KCF x c( )
CVSoil x( )
kN m2.5
1 νsoil x( )
2
3ρsratio x c( )
1
3
Dt x( )
6.3 Inline Vibration Onset Span Lengths
Simplify formulae me_ILz
me Ca kpz kpz 0 Leff_IL L x( ) Leff L KIL x 0 x EulILz
Eulerlimit KIL kpz 0 kpz Seffz 0
The frequency is a function of the loadcase (represented by x), the span length (L) and the environmental conditions (y). Static deflection ignored for inline direction
Inline Structural Frequency Section 6.7.2 Page 32 Ref. [1] Inline Onset Frequency Section 4.1.5 Page 23 Ref. [1]
IL1 L x( ) C1 1 CSF x( )E ls
KP x( )
me_ILKP x( )
Leff_IL L x( )4
1Seff
KP x( ) 0
Pcr Leff_IL L x( ) x
IL2 L x y( ) γf x 0 Uconset
KP x( ) yUwonset
KP x( ) y
VRILon L x 0 Dt x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 48/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
At the onset of VIV the two frequencies are equal. The other boolean expressions assist in making the calculation robust
Given Im L( ) 0= L 0m L EulILKP X( )
IL1 L X( ) IL2 L X Y( )= LILon L X Y( ) Find L( )
Find the minimum span length from the two environmental conditions for each loadcase
LILonerrz y
1000 m Lil 30m z 0=if
Lil LILonerrz 1 y
otherwise
Lil2 LILon Lil z KPStep y( )return
on error
IL2 15m 0.5km y 1.52
1.27
s1.00
LILon_matz y
LILonerrz y
0.999 Re
IL1 LILonerrz y
kpz IL2 LILonerr
z ykpz y
1.001if
1000m LILonerrz y
otherwise
LILonz
min LILon_matz 0
LILon_matz 1
Due to the nature of the equations specified by DNV, a solution is not always attainable. The Find command may not therefore always return a solution.
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 49/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 620.5
20.65
20.8
Inline Span Length (Onset Criteria)
Inline Vibration Onset Span Lengths
KP (km)
Min
imum
Allo
wabl
e Sp
an L
engt
h (m
)
Represent above results in graphical form
6.4 Crossflow Vibration Onset Span Lengths
Deflection Load per unit length, taken as weight per unit length qz c Wsubz c
Section 6.7.2 and Section 6.7.7 Page 32-33 Ref. [1]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 50/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Simplify formulae me_CF x( ) me CaCF VRCFon x 0 x 0 Leff_CF L x( ) Leff L KCF x 0 x EulCFz
Eulerlimit KCF kpz 0 kpz Seffz 0
Crossflow Structural Frequency
CF1 L x( ) C1 1 CSF x( )E ls
KP x( )
me_CF x( ) Leff_CF L x( )4
1Seff
KP x( ) 0
Pcr Leff_CF L x( ) x C3
C6
qKP x( ) 0 Leff_CF L x( )
4
E lsKP x( )
1 CSF x( )
1
1Seff
KP x( ) 0
Pcr Leff_CF L x( ) x
Dt x( )
2
Crossflow Onset Frequency CF2z y γf kpz 0 Uconset
z yUwonset
z y
VRCFon kpz 0 Dt kpz Section 4.1.5 Page 23 Ref. [1]
At the onset of VIV the two frequencies are equal. The other boolean expressions assist in making the calculation robust
Given L 0m CF1 L X( ) CF2KP X( ) Y= L EulCFKP X( )
Im L( ) 0=L
CF1 L X( )d
d0 LCFon L X Y( ) Find L( )
Solve to find onset length
LCFonerrz y
1000 m Lcf 30m z 0=if
Lcf LCFonerrz 1 y
otherwise
LCFon Lcf z KPStep y( )return
on error
LCFon_matz y
LCFonerrz y
0.999 Re
CF1 LCFonerrz y
kpz CF2z y
1.001if
1000m LCFonerrz y
otherwise
LCFonz
min LCFon_matz 0
LCFon_matz 1
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 51/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 626.6
26.75
26.9
CrossFlow Span Length (Onset Criteria)
Crossflow Vibration Onset Span Lengths
KP (km)
Min
imum
Allo
wabl
e Sp
an L
engt
h (m
)
6.0 SCREENING Screening Criteria
6.1 Inline
Compare Frequency calculation for effective span length and actual span length Section 2.3.3 Page 15 Ref. [1]
ILscr L x( )
UcscrKP x( )
VRILon L x 0 Dt x( )1 L
250 Dt x( )
1
ααscrKP x( )
γIL Range of Applicability Table 1.1
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 52/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Given Im L( ) 0= ILscr L X( ) IL1 L X( )= 0m Leff_IL L X( ) 200 Do X( ) L 0mL
IL1 L X( )d
d
0 L EulILKP X( )
Lilsc L X( ) Find L( )
LILscrerrz
1000 m Lil 25m z 0=if
Lil LILscrerrz 1
otherwise
Lilsc Lil z KPStep( )return
on error LILscrz
LILscrerrz
0.999 Re
ILscr LILscrerrz
kpz IL1 LILscrerr
zkpz
1.001if
1000m LILscrerrz
otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 53/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 622.3
22.35
22.4
22.45
22.5
Inline Span Length (Screening Criteria)
Inline Vibration Screening Span Lengths
KP (km)
Min
imum
Allo
wabl
e Sp
an L
engt
h (m
)
6.2 Crossflow
Crossflow screening requirement CFsrcz
Ucscrz
Uw_1z
VRCFon z KPStep 0 Dt z KPStep( )γCF Section 2.3.4 Page 15 Ref. [1]
Given CFsrcKP X( ) CF1 L X( )= L 0mL
CF1 L X( )d
d
0 L EulILKP X( )
Im L( ) 0= Lxfsc L X( ) Find L( )
LCFscrerrz
1 m Lcf 30m z 0=if
Lcf LCFscrerrz 1
otherwise
Lxfsc Lcf z KPStep( )return
on error LCFscrz
LCFscrerrz
0.999 Re
CF1 LCFscrerrz
z KPStep CFsrcz
1.001if
1000m LCFscrerrz
otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 54/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 625.8
25.838
25.875
25.913
25.95
Crossflow Span Length (Screening Criteria)
Crossflow Vibration Screening Span Lengths
KP (km)
Min
imum
Allo
wabl
e Sp
an L
engt
h (m
)
Screening Criteria
7.0 SIMPLIFIED ULS CRITERION CHECK ULS Criteria
7.1 Current Conditions
Dynamic stress calculations consider significant wave height and zero up-crossing period. Static (or instantaneous) stresses, are found using maximum wavevelocities and associated periods. Code requirement is that the worse of 100yr wave / 1yr current or 1yr wave / 100yr current is considered for the operating case(Section 2.5.5). 100 year return period can be reduced to 10 year if duration of loadcase is less than 6 months.
Currents Significant Wave velocity Significant Wave Heading
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 55/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
UcULSz y
Uc_1z
y 0=if
Uc_100z
LCinput 1=if
Uc_10z
otherwise
y 1=if
UwsigULSz y
Uw_1z
y 1=if
Uw_100z
LCinput 1=if
Uw_10z
otherwise
y 0=if
θrel_sigz y
θw_1_sig z KPStep( ) y 1=if
θw_100_sig z KPStep( ) LCinput 1=if
θw_10_sig z KPStep( ) otherwise
y 0=if
Spectral Peak Periods Maximum Wave Heading
TuULSz y
Tu_1z
y 1=if
Tu_100z
LCinput 1=if
Tu_10z
otherwise
y 0=if
θrel_maxz y
θw_1_max z KPStep( ) y 1=if
θw_100_max z KPStep( ) LCinput 1=if
θw_10_max z KPStep( ) otherwise
y 0=if
Single Wave Associated Period
UwmaxULSz y
Uw_max_1z
y 1=if
Uw_max_100z
LCinput 1=if
Uw_max_10z
otherwise
y 0=if
TwmaxULSz y
Tmax_1 z KPStep( ) y 1=if
Tmax_100 z KPStep( ) LCinput 1=if
Tmax_10 z KPStep( ) otherwise
y 0=if
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 56/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Combined Current Velocity UtotULSz y
UcULSz y
UwsigULSz y
Flow Regime Velocity ratio αULS x y( )
UcULSKP x( ) y
UtotULSKP x( ) y
KC No. KCuls x y( )
UwsigULSKP x( ) y
Dt x( )TuULS
KP x( ) y
Limiting span for whichresults can be found
Eulerlimit x( ) min 200 Do x( ) Eulerlimit KvSTAT x( ) x SeffKP x( ) 1
Unit Diameter Stress Amplitude
AIL L x( ) C4 L Leff L KvSTAT x( ) x( )( )1 CSF x( ) Dt x( ) Do x( ) tnom x( ) E
L2
Section 6.7.5 Page 33 Ref. [1]Inline
Cross - flow ACF L x( ) C4 L Leff L KvSTAT x( ) x( )( )1 CSF x( ) Dt x( ) Do x( ) tnom x( ) E
L2
7.2 Cross Flow Response Model Section 4.4.4 RP F105
Simplify Formulae meCFULS x( ) me CaCF VRCFon x 1 x 1 LeffCFULS L x( ) Leff L KCF x 1 x
CFULS L x( ) C1 1 CSF x( )E ls
KP x( )
meCFULS x( ) LeffCFULS L x( )4
1Seff
KP x( ) 1
Pcr LeffCFULS L x( ) x C3
C6
qKP x( ) 1 LeffCFULS L x( )
4
E lsKP x( )
1 CSF x( )
1
1Seff
KP x( ) 1
Pcr LeffCFULS L x( ) x
Dt x( )
2
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 57/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Reconstructing Figure 4-4 Section 4.4.3 Page 25 Ref. [1] Plateaux definition
Az1 x y( )
az1 0.9 fn12 15if
az1 0.9 0.5 fn12 1.5 1.5 fn12 2.3if
az1 1.3 2.3 fn12if
αULS x y( ) 0.8if
az1 0.9 KCuls x y( ) 30if
az1 0.7 0.01 KCuls x y( ) 10 10 KCuls x y( ) 30if
az1 0.7 KCuls x y( ) 10if
αULS x y( ) 0.8if
az1 Dt x( )
VRx L z y( ) 0
UtotULSz y
CFULS L z KPStep( ) Dt z KPStep( )γf z KPStep 1 on error
VRCF1 x y( ) 77 VRCFon x 1
1.151.3 Az1 x y( )
Dt x( )
VCFR2 x y( ) 167
13
Az1 x y( )
Dt x( )
Reduced velocity Section 4.1.5 Page 23 Ref. [1]
AyCF1 x y( )
2.0
VRCFon x 1
VRCF1 x y( )
VCFR2 x y( )
16
0
0.15
Az1 x y( )
Dt x( )
Az1 x y( )
Dt x( )
0
Vector representing five 'points'of Figure 4.4 Page 25 Ref. [1]
Translate the function into a matrix AyCF1z y
AyCF1 z KPStep y( )
Obtain a point along the 'curve' onFigure 4-4 Page 25 Ref. [1] for eachwave/current velocity
AyCF L z y( ) 0 VRx L z y( ) 2if
max 0 linterp AyCF1z y
0
AyCF1z y
1
VRx L z y( )
otherwise
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 58/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
7.3 Inline Response Model Section 4.3.5 Page 24 Ref. [1]
Correction for unsteadiness of flow Section 5.4.5 Page 29 Ref. [1] Correction for proximity to fixed boundary Section 5.4.6Page 30 Ref. [1]
ψKCα x y( )
0.85 0.15αULS x y( )
2 αULS x y( ) 0.5if
0.6 0.15 otherwise
KCuls x y( ) 40if
0.856
KCuls x y( )
αULS x y( )
2 αULS x y( ) 0.5if
0.66
KCuls x y( ) otherwise
40 KCuls x y( ) 5if
KCuls x y( )
51.05
αULS x y( )
2 1
αULS x y( ) 0.5if
KCuls x y( )
50.8 1 otherwise
otherwise
ψprox_CD x( ) 0.9
0.5
1 5e0 x( )
Dt x( )
e0 x( )
Dt x( )0.8if
1 otherwise
Correction for trenching effects Section 5.4.7Page 30 Ref. [1]
ψtrench_CD x( ) 12
3ΔID x( )
Correction for crossflow vibrations Section 5.4.8Page 30 Ref. [1]
ψVIV_CD L z y( ) 1 1.043 2 AyCF L z y( ) 0.65
Basic coefficient for steady flow Section 5.4.4Page 29 Ref. [1]
CdkD x( ) 0.65kpipe x( )
Dt x( )
104
if
0.6529
13
4
13log
kpipe x( )
Dt x( )
104 kpipe x( )
Dt x( )
102
if
1.05kpipe x( )
Dt x( )10
2if
Total Drag Coefficient Section 5.4.3 Page 29 Ref. [1]
CD L x y( ) CdkD x( ) ψKCα x y( ) ψprox_CD x( ) ψtrench_CD x( ) ψVIV_CD L KP x( ) y( )
Translate the function into a matrix
Structural frequency, Section 5.4.3Page 29 Ref. [1]
ILULS L x( ) C1 1 CSF x( )E ls
KP x( )
me Ca x( ) x 1 Leff L KIL x 1 x 4
1Seff
KP x( ) 1
Pcr Leff L KIL x 1 x x
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 59/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Design Reduced Velocity,Section 4.1.5 Page 23 Ref. [1] VRd L x y( ) 0
UtotULSKP x( ) y
ILULS L x( ) Dt x( )γf x 1
on error
Reduction Factor, Section 4.3.7Page 25 Ref. [1]
ψαIL x y( ) if αULS x y( ) 0.5 0 if 0.5 αULS x y( ) 0.8αULS x y( ) 0.5
0.3 1
Reconstructing Figure 4-2 Page 25 Ref. [1]
Reduction Factors
0 RIθ 1 RIθ1 x y( ) RIθ min 1 π2 π
22 θrel_sig
KP x( ) y
Ic 0.03 1
RIθ1 max RIθ 0
RIθ2 RIθ min 1Ic 0.03
0.17 1
RIθ2 max RIθ 0
Normalised VIV Amplitudes
Ay2 L x( ) 0.13 1min 1.799 Ksin L x 1
1.8
RIθ2
Dt x( ) Ay1 L x y( ) Dt x( ) max 0.18 1Ksin L x 1
1.2
RIθ1 x y( )Ay2 L x( )
Dt x( )
Cut-off Velocities VRIL1 L x y( ) 10Ay1 L x y( )
Dt x( )
VRILon L x 1 VRILend L x( ) if Ksin L x 1 1 4.5 0.8 Ksin L x 1 3.7
VRIL2 L x( ) VRILend L x( ) 2Ay2 L x( )
Dt x( )
Vector representing four'points' of Figure 4.2Page 25 Ref. [1]
AYOD L x y( )
VRILon L x 1
VRIL1 L x y( )
VRIL2 L x( )
VRILend L x( )
0
Ay1 L x y( )
Dt x( )
Ay2 L x( )
Dt x( )
0
Obtain a 'curve' on Figure 4-2 Page 25 Ref. [1] for each wave/current velocity
AyOD L x y( ) max 0 linterp AYOD L x y( )0
AYOD L x y( )1
Re VRd L x y( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 60/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
7.4 Stress Calculations
Crossflow dampingreduction factor
Rk L x( ) 1 0.15 Kscf L x 1 Kscf L x 1 4if
3.2 Kscf L x 1 1.5 Kscf L x 1 4if
Section 4.4.8 Page 26 Ref. [1]
Maximum inline unit diameter stress amplitude SIL L x y( ) 2 AIL L x( ) AyOD L x y( ) ψαIL x y( ) γs1 Section 4.3.3 Page 24 Ref.[1]
Maximum crossflow unit diameter stress amplitude SCF L x y( ) 2 ACF L x( ) AyCF L KP x( ) y( ) Rk L x( ) γs1 Section 4.4.3 Page 25 Ref. [1]
7.4.1 Inertia Force Coefficients
Basic Inertia Coefficient forfree concrete coated pipe
f α( ) 1.6 2 α α 0.5if
0.6 otherwise
Section 5.4.10Page 30 Ref. [1]
CMO x y( ) f αULS x y( ) 52 f αULS x y( ) KCuls x y( ) 5
Correction for Pipe RoughnessSection 5.4.11 Page 30 Ref. [1]
ψk_CM x( ) 0.75 0.434 logkpipe x( )
Dt x( )
Correction for TrenchEffects
ψtrench_CM x( ) 11
3ΔID x( )
Correction for Seabed Proximity Section 5.4.13 Page 30 Ref. [1] Total Coefficient of Inertia Section 5.4.9 Page 30 Ref. [1]
ψproxi_CM x( ) 0.840.8
1 5e0 x( )
Dt x( )
e0 x( )
Dt x( )0.8if
1 otherwise
CM x y( ) CMO x y( ) ψk_CM x( ) ψproxi_CM x( ) ψtrench_CM x( )
Translate the function into a matrix
Section 5.4.9 Page 30 Ref. [1] CMz y
CM z KPStep y( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 61/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
7.4.2 Peak Combined Drag and Inertia Loading This calculates the static load, and therefore considers the maximum wave and associated period
Horizontal Acceleration AmplitudeAwave z y( )
2 π
TwmaxULSz y
UwmaxULSz y
Wave Induced Velocity wrtWave Phase Angle
Wave Induced Acceleration wrtWave Phase Angle
Awave θ z y( ) Awave z y( )( ) sin θ( )Uwave θ z y( ) UwmaxULS
z y
cos θ( )
Drag Force wrt Wave Phase Angle Fdraguls L z y θ( )1
2ρw z KPStep( ) Dt z KPStep( ) CD L kpz y Uwave θ z y( ) UcULS
z y Uwave θ z y( ) UcULS
z y
Inertia Force wrt Wave Phase AngleFM z y θ( )
π
4ρw z KPStep( ) Dt z KPStep( ) 2 CM
z y Awave θ z y( )
Horizontal Force (Drag + Inertia)FH θ L z y( ) Fdraguls L z y θ( ) FM z y θ( )
The maximum horizontal hydrodynamicforce occurs when the first derivative isequal to zero.
FHmax L z y( ) fd1
2ρw z KPStep( ) Dt z KPStep( ) CD L kpz y
fmπ
4ρw z KPStep( ) Dt z KPStep( ) 2 CM
z y
fhi fd Uwave θ z y( ) UcULSz y
Uwave θ z y( ) UcULSz y
fm Awave θ z y( )
i i 1
θ 0deg 2deg 90degfor
max fh( )return
Static Span effective LengthLeffULS L x( ) Leff L KvSTAT x( ) x( )
Resultant Moment Mwave L x y( ) C5 L LeffULS L x( ) FHmax L KP x( ) y( ) LeffULS L x( )
2
1Seff
KP x( ) 1
Pcr LeffULS L x( ) x
Section 6.7.6 / 6.7.10 Page 33 Ref. [1]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 62/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Associated Stress σFM_MAX L x y( )Mwave L x y( ) Do x( ) t2 x( )
2 lsKP x( )
Section 2.5.8 Page 17 Ref. [1]
σdynIN L x y( )1
2max 0.4 SCF L x y( )
AIL L x( )
ACF L x( ) SIL L x y( )
σFM_MAX L x y( )Dynamic Inline Bending Stress Section 2.5.12 Page 18 Ref. [1]
Dynamic Crossflow Bending Stress σdynCF L x y( )1
2SCF L x y( ) Section 2.5.8 Page 17 Ref. [1]
7.4.3 Peak Combined Drag and Inertia Loading
Calculates the static load, and therefore considers the maximum wave and associated period
Static, Functional [Vertical] BendingMoment due to Submerged Weight
Mfunc L x( ) C5 L LeffULS L x( ) Wsub
KP x( ) 1LeffULS L x( )
2
1Seff
KP x( ) 1
Pcr LeffULS L x( ) x
γfLC γc Section 6.7.10 Page 33 Ref. [1]
Environmental [Horizontal] BendingMoment due to in-line VIV
Section 2.5.7 / Section 2.5.8 Page 17 Ref. [1]MDILVIV L x y( ) σdynIN L x y( )
2 lsKP x( )
Do x( ) tnom x( )
2
γE
Environmental [Vertical] Bending Moment due to cross-flow VIV
MDCFVIV L x y( ) σdynCF L x y( )
2 lsKP x( )
Do x( ) tnom x( )
2
γE Section 2.5.7 / Section 2.5.8 Page 17 Ref. [1]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 63/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
7.5 Preliminary Load-Controlled Combined Loading Check Calculations
Operating Temperature for Stress De-Rating (Valid for Toper < 200 oC)
Yield strength temperature de-rating Taken from Section 5, B604 if no other information exists
Yield Stress Temperature De-rating fy_temp x( ) ifTULS x( )
°C50 0 if
TULS x( )
°C100
TULS x( )
°C50
0.6TULS x( )
°C100
0.4
30
MPa
Tensile Stress Temperature De-rating fu_temp x( ) ifTULS x( )
°C50 0 if
TULS x( )
°C100
TULS x( )
°C50
0.6TULS x( )
°C100
0.4
30
MPa
Characteristic Yield Strength fy x( ) SMYS fy_temp x( ) αU Equation 5.5 Section 5 C302 - Page 44 Ref. [2]
Characteristic Tensile Strength fu x( ) SMTS fu_temp x( ) αU Equation 5.6 Section 5 C302 - Page 44 Ref. [2]
Design Moment MSd L x y( ) Mfunc L x( ) MDCFVIV L x y( ) 2 MDILVIV L x y( )2
Equation 4.5 Section 4 G201 - Page 39 Ref. [2]
Design differential effective axoiavle froprrceessure SSd x( ) SeffKP x( ) 1
γfLC γc Equation 4.7 Section 4 G201 - Page 39 Ref. [2]
Design differential overpressure Δpd x( ) pldULS x( ) Pe x( )
Characteristic plasticmoment resistance
Mp x( ) fy x( ) Do x( ) t2 x( ) 2 t2 x( ) Equation 5.21 Section 5 D605 - Page 48 Ref. [2]
Characteristic plastic axialforce resistance
Sp x( ) fy x( ) π Do x( ) t2 x( ) t2 x( ) Equation 5.20 Section 5 D605 - Page 48 Ref. [2]
fcb x( ) min fy x( )fu x( )
1.15
Limit strength Equation 5.9 Section 5 D202 - Page 38 Ref. [2]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 64/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
pb x( )2 t2 x( )
Do x( ) t2 x( )fcb x( )
2
3
Yield Limit State Equation 5.8 Section 5 D202 - Page 38 Ref. [2]
Plastic Collapse Pressure pp x( ) fy x( ) αfab2 t2 x( )
Do x( ) Equation 5.11 Section 5 D401 - Page 46 Ref. [2]
7.6 Internal Overpressure
Equation 5.24 - Section 5 D605 Page 48Ref. [2]
Flow stress parameter Account for effect of D/t ratio
βio x( ) beta 0.5Do x( )
t2 x( )15if
beta
60Do x( )
t2 x( )
90 15
Do x( )
t2 x( ) 60if
beta 0Do x( )
t2 x( )60if
αc_io x( ) 1 βio x( ) βio x( )fu x( )
fy x( ) αp2 x( ) 1 βio x( )
pldULS x( ) Pe x( )
pb x( )0.7if
1 3 βio x( ) 1pldULS x( ) Pe x( )
pb x( )
otherwise
Equation 5.22 - Section 5 D605Page 48 Ref. [2]
Equation 5.23 - Section 5 D605 Page 48 Ref. [2]
Interaction Ratio Equation 5.19(a) -Section 5 D607 Page 47 Ref. [2] UCio L x y( ) γm γSC
MSd L x y( )
αc_io x( ) Mp x( )
γm γSC SSd x( )
αc_io x( ) Sp x( )
2
2
αp2 x( )pldULS x( ) Pe x( )
αc_io x( ) pb x( )
2
Design Moment forInternal Overpressure MDio x( )
1 αp2 x( )pldULS x( ) Pe x( )
αc_io x( ) pb x( )
2
γm γSC SSd x( )
αc_io x( ) Sp x( )
2
γm γSCαc_io x( ) Mp x( )
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 65/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
7.7 External Overpressure
Elastic Collapse PressureCharacteristic Collapse Pressure Equation 5.10 - Section 5 D401 Page 46
Ref. [2]Equation 5.11 - Section 5 D401Page 46 Ref. [2] guess pc 1barg
pel x( )
2 Et2 x( )
Do x( )
3
1 ν2
pc x( ) root pc pel x( ) pc2
pp x( )2
pc pel x( ) pp x( ) f0
Do x( )
t2 x( ) pc
Interaction Ratio Equation 5.28(a) - Section 5 D607Page 48 Ref. [2]UCeo L x y( ) γm γSC
MSd L x y( )
αc_io x( ) Mp x( )
γm γSC SSd x( )
αc_io x( ) Sp x( )
2
2γm γSC Pe x( ) 0
pc x( )
2
Design moment forexternal overpressure
MDeo x( )
1γm γSC Pe x( ) 0
pc x( )
2
γm γSC SSd x( )
αc_io x( ) Sp x( )
2
γm γSCαc_io x( ) Mp x( )
7.8 Results
Select internal or external overpressure UC L x y( ) if pldULS x( ) Pe x( ) UCio L x y( ) UCeo L x y( )
and associated moment Md x( ) if pldULS x( ) Pe x( ) MDio x( ) MDeo x( )
Solve to find Given Im Lu( ) 0= UC Lu X Y( ) 1= Lu 1m Mfunc Lu X( ) 0 LlimULS Lu X Y( ) Find Lu( )
LULSz y 1 m LU LCFon0 z 0=if
LU LULSz 1 y
otherwise
luls LlimULS LU z KPStep y( )
luls
on error LULSz
min LULSz 0 LULS
z 1
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 66/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
0 2 4 647.5
47.6
47.7
47.8
47.9
48
Span Length (ULS Criteria)
Span Lengths Following ULS Criterion
KP (km)
Min
imum
Allo
wabl
e Sp
an L
engt
h (m
)
ULS Criteria
8.0 VALIDITY CHECKS / RESULT PROCESSING
Validity Checks / Result Collation / Data Saving
8.1 Validity Checks
Maximum length for response model validity MaxmODL x( ) 140 Do x( ) Section 6.7.1 Page 32 Ref [1]
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 67/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
Crossflow deflection δCF x z( ) C6
Wsubz 0
LCFonz
4
E lsKP x( )
1 CSF x( ) 1 C2
Seffz 0
LCFonz
2
1 CSF x( ) π2
E lsKP x( )
1
Section 6.7.7 Page 33 Ref [1]
Max allowable deflection δcheck x z( ) if δCF x z( ) 2.5 Dt x( ) "Invalid" "" Section 6.7.1 Page 32 Ref [1]
Section 6.7.1 Page 32 Ref [1]Check that Euler buckling is not influencing EulerIL x z( ) "" if
Seffz 0
Pcr LILonz
x 0.5 "" "Influenced by Euler limit"
on error
EulerCF x z( ) "" if
Seffz 0
Pcr LCFonz
x 0.5 "" "Influenced by Euler limit"
on error
Bar buckling influenceon screening spans
eulils x z( ) if
Seffz 0
Pcr LILscrz
x 0.5 "" "Influenced by Euler limit"
eulcfs x z( ) if
Seffz 0
Pcr LCFscrz
x 0.5 "" "Influenced by Euler limit"
Model length validity limiton onset spans
mlilo x z( ) if LILonz
200 Do x( ) ">200Do limit" ""
mlcfo x z( ) if LCFonz
200 Do x( ) ">200Do limit" ""
Model length validity limiton screening spans
mlils x z( ) if LILscrz
200 Do x( ) ">200Do limit" ""
mlcfs x z( ) if LCFscrz
200 Do x( ) ">200Do limit" ""
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 68/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
If current flow ratio lessthan 0.5 inline VIV can beignored
ILVIVo z( ) if ααonz 0
0.5 "a<0.5 - IL VIV may be ignores" ""
Section 1.9.1 Page 10 Ref [1]
ILVIVs z( ) if ααscrz
0.5 "a<0.5 - IL VIV may be ignores" ""
If D/t > 45, Load Controlled Check not Valid
Determine which combination of environmental loading has been used bb z( ) 0 LULSz
LULSz 0=if
1 otherwise
zz z( ) 0 LILonz
LILon_matz 0
=if
1 otherwise
Include in results table z 0 1 Length
KPStep KPz z KPStep Dtv
zif
Do KPz tnom KPz 45 "OK" "Invalid D/t ratio"
lilonz if concat mlilo KPz z EulerIL KPz z ILVIVo z( ) ""= "OK" concat mlilo KPz z EulerIL KPz z ILVIVo z( )
lilscrz if concat mlils KPz z eulils KPz z ILVIVs z( ) ""= "OK" concat mlilo KPz z EulerCF KPz z ILVIVs z( )
lcfonz if concat mlcfo KPz z EulerCF KPz z δcheck KPz z ""= "OK" concat mlcfo KPz z EulerCF KPz z δcheck KPz z aaz KPz
lcfscrz if concat mlcfs KPz z eulcfs KPz z ""= "OK" concat mlcfs KPz z eulcfs KPz z
Create large matrix to pass to output table
results augment KP LILon LCFon lilon lcfon LILscr LCFscr lilscr lcfscr LULS Dtv
Validity Checks / Result Collation / Data Saving
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 69/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
9.0 RESULTS
Location for Detailed Span results Location 5km
Extract Data for Desired Location
loc roundLocation
KPStep
SpanVIVloc stack LILonloc
LCFonloc
LILscrloc
LCFscrloc
"NA"
Menv L x y( ) MDCFVIV L x y( )
2MDILVIV L x y( )
2
SpanULSloc stack "NA" "NA" "NA" "NA" LULSloc
Spansloc augment SpanVIVloc SpanULSloc
VIVloc stack
Seffloc 0
kN
Uconsetloc zz loc( )
m s1
Uwonset
loc zz loc( )
m s1
ααonloc 0
Wsub
loc 0
kN m1
CSF loc KPStep( ) VRILon LILonloc
loc KPStep 0
VRCFon loc KPStep 0 δCF loc KPStep zz loc( )( )
m
2.5
ULSloc stack
Mfunc LULSloc
loc KPStep kN m
Menv LULSloc
loc KPStep bb loc( ) kN m
MSd LULS
locloc KPStep bb loc( ) kN m
Seff
loc 1
kN
UcULSloc bb loc( )
m s1
UwmaxULS
loc bb loc( )
m s1
Eulerlimit KCF loc KPS
SaveLC LCinput 1 0.00 SaveBC BC 1 2.00 SaveSEFF Seffinput 1 0.00
SaveSteelRough roughness 1 2.00 SaveSpan_Def Span_Def 1 2.00 SaveWall Wall 1 1.00
Extract Data for Desired Location
9.1 Tabulated Span Lengths
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 70/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
freespan
INLINE CROSSFLOW INLINE CROSSFLOW
0 22.45 25.92 OK OK 47.91 OK
100 22.45 25.91 OK OK 47.89 OK
200 22.45 25.91 OK OK 47.91 OK
300 22.46 25.92 OK OK 47.93 OK
400 22.47 25.93 OK OK 47.96 OK
500 22.46 25.92 OK OK 47.93 OK
600 22.44 25.91 OK OK 47.88 OK
700 22.45 25.91 OK OK 47.89 OK
800 22.45 25.92 OK OK 47.91 OK
900 22.44 25.90 OK OK 47.87 OK
1000 22.42 25.88 OK OK 47.82 OK
1100 22.42 25.88 OK OK 47.82 OK
ULS RESULTS
CHECKKP
SCREENING SPAN LIMITSSCREENING RESULTS
CHECK ULS SPAN LIMITS
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 71/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
results
9.2 Charted Span Lengths
0 2 4 60
10
20
30
40
Inline Screening Span LengthsCrossflow Screening Span LengthsULS Span Lengths
Summary of Allowable Spans Lengths
Distance Along Pipe (km)
Min
imum
Allo
wabl
e Sp
an L
engt
h (m
)
LILscrz
LCFscrz
LULSz
kpz
km
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 72/73
APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE
9.3 Detailed Results at Specified Location
SU TU NAU FIELD DEVELOPMENT
As-Laid Case
12inch Production Pipeline from STN-N (KP0) to STN-S (KP6.55)
VIV ULS
m 22.35 NA
m 25.81 NA
m NA 47.59
0.50
VRILon m/s 1.18
Crossflow Onset [Reduced] Velocity
Concrete Stiffness Factor
VRCFon m/s 2.19
CSF
0.21
Maximum Allowable Span Length at Location Specified Symbol
Inline Onset [Reduced] Velocity
-----
Submerged Weight
Crossflow Screening Allowable Span Length
ULS Allowable Span Length
----
Wsub
PROJECTLOADCASEPIPELINE DESCRIPTION
Onset Steady Current Velocity Uc m/s
Effective Axial Force
0.99
Onset Wave Induced Velocity Uw m/s 0.62
Onset current flow ratio αα 0.25
kN/m
Unit
VIV Onset Allowabe Spans
LULS
Load Case
ValueSymbol Unit
Inline Screening Allowable Span Length LILscr
LCFscr
Sef f op kN 0.00
MPa 15.92
σCF m 0.04
Allowable Deflection
Crossflow Onset Deflection
Crossflow Soil Stiffness KV MPa 21.04
Inline Soil Stiffness
σmax m 1.26
KL
0.99
-4.16
Submerged Weight
Pressure Difference
3.51
2.82
Drag Coefficient
Inertia Coefficient
Euler Buckling Limit
ULS Allowabl Spans
ValueUnitSymbol
Functional moment
357.09
0.00
0.48
0.30
Environmental moment
Design moment
Effective Axial Force
Steady Current Velocity
Maximum Wave Velocity
64.78
kN.m
kN.m
kN.m
kN
m/s
m/s
m
193.24
210.21
Mf
Me
Md
Sef f ULS
Uc
Uw
----
CD
Cm
Wsub
ΔP
----
----
kN/m
bar
Detailed_Results "Updated Successfully"
Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 73/73