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![Page 1: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/1.jpg)
OTC 23033A Holistic Approach to Steady-State Heat Transfer
from Partially and Fully Buried Pipelines
Erich Zakarian
James Holbeach
Julie Morgan
![Page 2: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/2.jpg)
Background
Pipe
Pipeline embedment into the seabed may affect the integrity of production systems
Partial burial of offshore pipelines may be caused by seabed mobility, sediment flow, trench collapse, cyclic pipe motions under wave action, lateral buckling, etc.
Seabed
![Page 3: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/3.jpg)
Reduced heat loss from high temperature fluids• Hotter temperature profiles for longer
Uncontrolled pipeline lateral buckling• Under design of cooling spools
Accelerated degradation of external coatingsTop of line corrosion in wet gas pipelines
Reduced heat gain from seawater in gas transport• Excessive Joule-Thomson cooling
Condensate and water drop-out, corrosion, hydrate formation, frost heaving
Potential Issues
![Page 4: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/4.jpg)
Steady-State Heat Transfer
H Dext
bSeabed Q = U.A.T
Q = heat transfer rate [W]A = pipe surface area [m2]T = Tfluid - Tamb [K]U = overall heat transfer coefficient (OHTC) [W/m2/K]
Tamb
Tfluid
![Page 5: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/5.jpg)
Buried Pipe OHTC
Dext = outer diameter of external coatings [m]Dsteel = outer diameter of steel wall [m]Din = inner diameter of pipe [m]Uwall = pipe wall U-value [W/m2/K]hsoil = wall to soil heat transfer coefficient [W/m2/K]hin = inside fluid film coefficient [W/m2/K] hamb = ambient fluid film coefficient [W/m2/K]
![Page 6: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/6.jpg)
H
Seabed
Dext
ksoil = soil thermal conductivity [W/m/K]hsoil = wall to soil heat transfer coefficient (HTC) [W/m2/K]Dext = outer diameter of pipe wall and external coatings [m]H = burial depth to pipe centerline [m]
Only valid for H > Dext/2Inaccurate formula at shallow burial depths
Wall to Soil HTC
e.g. Carslaw & Jaeger (1959)
![Page 7: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/7.jpg)
Analytical SolutionsFour explicit, continuous formulae for the OHTC were compared to 3 independent sources of Computational
Fluid Dynamics (CFD) analyses
Formulae CFD analyses
•Carslaw & Jaeger (1959) •Morud & Simonsen (2007)•Ovuworie (2010) •OTC 23033 (2012)
•Morud & Simonsen (2007)
•MSi Kenny (2011)•Frazer-Nash (2011)
![Page 8: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/8.jpg)
Typical Pipe Wall U-valuesTransport system Typical pipe wall
U-value [W/m2/K]
Pipe-in-pipe system Highly insulated pipeline Flexible flowline
0.5 to 15
Insulated pipeline Concrete weight coated pipeline 15 to 50
Uninsulated pipeline Cooling spool 50 to 1500+
5.68 W/m2/K = Btu/ft2/h/F
![Page 9: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/9.jpg)
Pipe Biot Number
Bip = (dimensionless) pipe Biot number [-]Uwall = pipe wall U-value [W/m2/K]ksoil = soil thermal conductivity [W/m/K]Dref = reference diameter of the OHTC [m]
![Page 10: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/10.jpg)
Holistic ApproachTransport system Typical
pipe Biot number [-]
Pipe-in-pipe system Highly insulated pipeline Flexible flowline
Up to 4
Insulated pipeline Concrete weight coated pipeline 4 to 50
Uninsulated pipeline Cooling spool Above 50
![Page 11: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/11.jpg)
0
2
4
6
8
10
12
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
OH
TC [W
/m2/
K]
Burial depth [%]
OHTC vs. Burial Depth
0%
100%
200%
50%
![Page 12: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/12.jpg)
Transport system Typical pipe Biot number [-]
Pipe-in-pipe system Highly insulated pipeline Flexible flowline
Up to 4
Insulated pipeline Concrete weight coated pipeline 4 to 50
Uninsulated pipeline Cooling spool Above 50
Low Pipe Biot Number
![Page 13: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/13.jpg)
0
2
4
6
8
10
12
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
OH
TC [W
/m2/
K]
Burial depth [%]
Carslaw & Jaeger
Morud & Simonsen
Ovuworie
OTC 23033
CFD (CFX 12.1)
14’’ Insulated Pipeline
Bip= 2.1
10% error bar
![Page 14: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/14.jpg)
Intermediate Pipe Biot Number
Transport system Typical pipe Biot number [-]
Pipe-in-pipe system Highly insulated pipeline Flexible flowline
Up to 4
Insulated pipeline Concrete weight coated pipeline 4 to 50
Uninsulated pipeline Cooling spool Above 50
![Page 15: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/15.jpg)
0
5
10
15
20
25
30
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
OH
TC [W
/m2/
K]
Burial [%]
Carslaw & Jaeger
Morud & Simonsen
Ovuworie
OTC 23033
CFD (FLUENT 6.2)
40’’ Trunkline
Bip= 4.2
10% error bar
![Page 16: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/16.jpg)
High Pipe Biot NumberTransport system Typical
pipe Biot number [-]
Pipe-in-pipe system Highly insulated pipeline Flexible flowline
Up to 4
Insulated pipeline Concrete weight coated pipeline 4 to 50
Uninsulated pipeline Cooling spool Above 50
![Page 17: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/17.jpg)
0
100
200
300
400
500
600
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
OH
TC [W
/m2/
K]
Burial [%]
Carslaw & Jaeger
Morud & Simonsen
Ovuworie
OTC 23033
CFD (FLUENT 13.0)
24’’ Wet Gas Cooling Section
Bip= 441.2
10% error bar
![Page 18: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/18.jpg)
And what about onshore pipelines?
![Page 19: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/19.jpg)
Onshore Pipelines
Big = ground Biot number [-]hamb = ambient fluid film coef. [W/m2/K]Dref = reference diameter [m]ksoil = soil thermal conductivity [W/m/K]
Environment Typical ambient fluid film coef. [W/m2/K]
Typical groundBiot number [-]
Onshore 4 to 30 Up to 15
Offshore 200 to 1000+ Above 50
![Page 20: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/20.jpg)
0
2
4
6
8
10
12
14
16
18
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
OH
TC [W
/m2/
K]
Burial [%]
Carslaw & Jaeger
Morud & Simonsen
Morud & Simonsen (original)
Ovuworie
OTC 23033
40’’ Onshore Trunkline
Bip= 17.3 Big= 2.3
![Page 21: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/21.jpg)
ConclusionsAn OHTC accuracy of 10% or less relative to CFD can be achieved with analytical formulae for a comprehensive range of:
• Offshore pipeline systems• Soil thermal conductivities• Burial depths
![Page 22: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/22.jpg)
Conclusions• Explicit, continuous formulae can be used for quickly generating profiles of overall heat transfer coefficient (OHTC) along partially and fully buried pipelines • The effect of input data uncertainties on steady-state pipeline heat transfer can easily be assessed for any amount of burial
![Page 23: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/23.jpg)
Recommended FormulaeTransport system Environment Recommended
formulae Pipe-in-pipe system Highly insulated pipeline Flexible flowline
Offshore•Morud & Simonsen•OTC 23033Onshore
Insulated pipeline Concrete weight coated pipeline
Offshore •Morud & Simonsen•OTC 23033
Onshore •Ovuworie•OTC 23033
Uninsulated pipeline Cooling spool
Offshore•Morud & Simonsen•Ovuworie•OTC 23033
Onshore •Ovuworie•OTC 23033
![Page 24: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/24.jpg)
OTC 23033A Holistic Approach to Steady-State Heat Transfer from
Partially and Fully Buried Pipelines
Erich Zakarian
James Holbeach
Julie Morgan
![Page 25: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/25.jpg)
0
2
4
6
8
10
12
14
16
18
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
OH
TC [W
/m2/
K]
Burial [%]
Carslaw & Jaeger
Morud & Simonsen
Ovuworie
OTC 23033
CFD (FLUENT 13.0)
Bip= 9.5
42’’ Offshore Trunkline
![Page 26: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/26.jpg)
CFD Model Setup (Frazer-Nash)
• Domain extends ~ 20 Dext in all directions for all cases
• SST k-ω turbulence model• Roughness = 10mm (seabed), 2.5 μm (TLPP), 250 μm (CWC)
![Page 27: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/27.jpg)
Boundary Layer Velocity Profiles
• Inflow profiles are based on the Atmospheric Boundary Layer theory, modified for application at the seabed• Fitted to measured sea current velocities (2.6 m above the seabed)
![Page 28: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/28.jpg)
0102030405060708090
100110120130
0 10 20 30 40 50 60 70 80 90 100
Flui
d te
mpe
ratu
re [°
C]
Distance [km]
OHTC = 5.8 W/m2/K (Ovuworie)
OHTC = 6.9 W/m2/K (Morud & Simonsen)
OHTC = 7 W/m2/K (CFD)
OHTC = 7.2 W/m2/K (OTC 23033)
OHTC = 8.5 W/m2/K (Carslaw & Jaeger)
OHTC = 10 W/m2/K (No burial)
14’’ Insulated Pipeline
Burial = 50%
![Page 29: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/29.jpg)
0
10
20
30
40
50
60
70
80
90
100
110
120
0 5 10 15 20
Flui
d te
mpe
ratu
re [°
C]
Distance [km]
Burial = 0% (OHTC = 244.7 W/m2/K)Burial = 25% (OHTC = 166.4 W/m2/K)Burial = 50% (OHTC = 126.7 W/m2/K)Burial = 75% (OHTC = 87.6 W/m2/K)Burial = 90% (OHTC = 58.6 W/m2/K)Burial = 99% (OHTC = 32.4 W/m2/K)
24’’ Wet Gas Cooling Section
hamb 300 W/m2/K
![Page 30: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/30.jpg)
0
10
20
30
40
50
60
70
80
90
100
110
120
0 5 10 15 20
Flui
d te
mpe
ratu
re [°
C]
Distance [km]
Burial = 0% (OHTC = 508.9 W/m2/K)Burial = 25% (OHTC = 336.4 W/m2/K)Burial = 50% (OHTC = 252.6 W/m2/K)Burial = 75% (OHTC = 173.3 W/m2/K)Burial = 90% (OHTC = 115.2 W/m2/K)Burial = 99% (OHTC = 50.5 W/m2/K)
24’’ Wet Gas Cooling Section
hamb 800 W/m2/K
![Page 31: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/31.jpg)
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120 140 160 180 200
Flui
d te
mpe
ratu
re [°
C]
Distance [km]
OHTC = 13.1 W/m2/K (Ovuworie)
OHTC = 14.8 W/m2/K (Morud & Simonsen)
OHTC = 15.3 W/m2/K (CFD)
OHTC = 15.6 W/m2/K (OTC 23033)
OHTC = 20.3 W/m2/K (Carslaw & Jaeger)
OHTC = 23.4 W/m2/K (No burial)
40’’ Trunkline
Burial = 50%
![Page 32: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/32.jpg)
Ambient Temperature
Small seasonal variation of ambient temperature (e.g. deep offshore)
Tamb = Tsea Tsoil (steady-state heat transfer)
Large seasonal variation of ambient temperature (e.g. onshore)
Tamb = Tsoil ≠ Tair (no steady-state heat transfer)
![Page 33: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/33.jpg)
r
At the pipe external surface (r = Dext/2)
At the ground surface (y = 0)
Mixed Boundary Conditions
y
x
![Page 34: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/34.jpg)
Burial Depth
H
Seabed
Dext
![Page 35: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/35.jpg)
Ambient Film Coefficient
500
600
700
800
900
1000
1100
0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%
h ext
[W/m
2/K]
Burial [%]
External heat transfer coefficient24-in Wet Gas Cooling Section
PIPESIM 2009(current speed 0.1 m/s)
CFD (FLUENT)(current speed 0.1 m/s)
PIPESIM 2009(current speed 0.01 m/s)
CFD (FLUENT)(current speed 0.01 m/s)
![Page 36: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/36.jpg)
24’’ Wet Gas Cooling Section Contour plot of temperature [K]
for 50% burial
![Page 37: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/37.jpg)
24’’ Wet Gas Cooling Section Contour plot of temperature [K]
for 95% burial
![Page 38: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/38.jpg)
42’’ Offshore TrunklineContour plot of temperature [°C]
for 50% burial
![Page 39: OTC 23033](https://reader035.fdocuments.net/reader035/viewer/2022062405/55622c1dd8b42ab6588b5472/html5/thumbnails/39.jpg)
42’’ Offshore TrunklineContour plot of temperature [°C]
for 95% burial