1. OTC 23033
A Holistic Approach to Steady-State Heat Transfer
from Partially and Fully Buried Pipelines
Erich Zakarian
James Holbeach
Julie Morgan

2. Background
Partial burial of offshore pipelines may be caused by
seabed mobility, sediment flow, trench collapse, cyclic
pipe motions under wave action, lateral buckling, etc.
Pipe
Seabed
Pipeline embedment into the seabed may affect
the integrity of production systems

3. Potential Issues
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 coatings
Top 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

4. Steady‐State Heat Transfer
Tamb Q = U.A.T
b Seabed
Q = heat transfer rate [W]
H Dext A = pipe surface area [m2]
Tfluid T = Tfluid ‐ Tamb [K]
U = overall heat transfer
coefficient (OHTC) [W/m2/K]

5. 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]

6. Wall to Soil HTC
Seabed
H
Dext
e.g. Carslaw & Jaeger (1959)
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/2
Inaccurate formula at shallow burial depths

7. Analytical Solutions
Four 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)
• Morud & Simonsen (2007)
• MSi Kenny (2011)
• Ovuworie (2010)
• Frazer‐Nash (2011)
• OTC 23033 (2012)

8. Typical Pipe Wall U‐values
Typical pipe wall
Transport system
U‐value [W/m2/K]
 Pipe‐in‐pipe system
 Highly insulated pipeline 0.5 to 15
 Flexible flowline
 Insulated pipeline
15 to 50
 Concrete weight coated pipeline
 Uninsulated pipeline
50 to 1500+
 Cooling spool
5.68 W/m2/K = Btu/ft2/h/F

9. 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]

10. Holistic Approach
Typical
Transport system
pipe Biot number [‐]
 Pipe‐in‐pipe system
 Highly insulated pipeline Up to 4
 Flexible flowline
 Insulated pipeline
4 to 50
 Concrete weight coated pipeline
 Uninsulated pipeline
Above 50
 Cooling spool

11. OHTC vs. Burial Depth
12 0%
10 50%
OHTC [W/m2/K]
8
100%
6
4
200%
2
0
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
Burial depth [%]

12. Low Pipe Biot Number
Typical
Transport system
pipe Biot number [‐]
 Pipe‐in‐pipe system
 Highly insulated pipeline Up to 4
 Flexible flowline
 Insulated pipeline
4 to 50
 Concrete weight coated pipeline
 Uninsulated pipeline
Above 50
 Cooling spool

13. 14’’ Insulated Pipeline
12
Carslaw & Jaeger
10% error bar
10 Morud & Simonsen
Ovuworie
OHTC [W/m2/K]
8
OTC 23033
6 CFD (CFX 12.1)
4
2
Bip= 2.1
0
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
Burial depth [%]

14. Intermediate Pipe Biot Number
Typical
Transport system
pipe Biot number [‐]
 Pipe‐in‐pipe system
 Highly insulated pipeline Up to 4
 Flexible flowline
 Insulated pipeline
4 to 50
 Concrete weight coated pipeline
 Uninsulated pipeline
Above 50
 Cooling spool

15. 40’’ Trunkline
30
Carslaw & Jaeger
25 10% error bar Morud & Simonsen
Ovuworie
OHTC [W/m2/K]
20
OTC 23033
15 CFD (FLUENT 6.2)
10
5
Bip= 4.2
0
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
Burial [%]

16. High Pipe Biot Number
Typical
Transport system
pipe Biot number [‐]
 Pipe‐in‐pipe system
 Highly insulated pipeline Up to 4
 Flexible flowline
 Insulated pipeline
4 to 50
 Concrete weight coated pipeline
 Uninsulated pipeline
Above 50
 Cooling spool

17. 24’’ Wet Gas Cooling Section
600
Carslaw & Jaeger
500 Morud & Simonsen
10% error bar Ovuworie
OHTC [W/m2/K]
400
OTC 23033
300 CFD (FLUENT 13.0)
200
100
Bip= 441.2
0
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
Burial [%]

18. And what about
onshore pipelines?

19. Onshore Pipelines
Typical ambient fluid Typical ground
Environment
film coef. [W/m2/K] Biot number [‐]
Onshore 4 to 30 Up to 15
Offshore 200 to 1000+ Above 50
Big = ground Biot number [‐]
hamb = ambient fluid film coef. [W/m2/K]
Dref = reference diameter [m]
ksoil = soil thermal conductivity [W/m/K]

20. 40’’ Onshore Trunkline
18
Carslaw & Jaeger
16
Morud & Simonsen
14 Morud & Simonsen (original)
OHTC [W/m2/K]
12 Ovuworie
OTC 23033
10
8
6
4
Bip= 17.3
2
Big= 2.3
0
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
Burial [%]

21. Conclusions
An 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

22. 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

23. Recommended Formulae
Recommended
Transport system Environment
formulae
 Pipe‐in‐pipe system Offshore • Morud & Simonsen
 Highly insulated pipeline • OTC 23033
 Flexible flowline Onshore
 Insulated pipeline Offshore
• Morud & Simonsen
• OTC 23033
 Concrete weight coated • Ovuworie
 pipeline Onshore • OTC 23033
• Morud & Simonsen
 Uninsulated pipeline Offshore • Ovuworie
• OTC 23033
 Cooling spool • Ovuworie
Onshore • OTC 23033

24. OTC 23033
A Holistic Approach to Steady‐State Heat Transfer from
Partially and Fully Buried Pipelines
Erich Zakarian
James Holbeach
Julie Morgan

25. 42’’ Offshore Trunkline
18
Carslaw & Jaeger
16
Morud & Simonsen
14
Ovuworie
OHTC [W/m2/K]
12 OTC 23033
10 CFD (FLUENT 13.0)
8
6
4
2 Bip= 9.5
0
0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%
Burial [%]

26. 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)

27. 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)

28. 14’’ Insulated Pipeline
130
120 OHTC = 5.8 W/m2/K (Ovuworie)
110 OHTC = 6.9 W/m2/K (Morud & Simonsen)
100 OHTC = 7 W/m2/K (CFD)
Fluid temperature [°C]
90 OHTC = 7.2 W/m2/K (OTC 23033)
80 OHTC = 8.5 W/m2/K (Carslaw & Jaeger)
70 OHTC = 10 W/m2/K (No burial)
60
50
40
30
20
10 Burial = 50%
0
0 10 20 30 40 50 60 70 80 90 100
Distance [km]

29. 24’’ Wet Gas Cooling Section
120
Burial = 0% (OHTC = 244.7 W/m2/K)
110
Burial = 25% (OHTC = 166.4 W/m2/K)
100 Burial = 50% (OHTC = 126.7 W/m2/K)
Fluid temperature [°C]
90 Burial = 75% (OHTC = 87.6 W/m2/K)
80 Burial = 90% (OHTC = 58.6 W/m2/K)
Burial = 99% (OHTC = 32.4 W/m2/K)
70
60
50
40
30
20
10
0
hamb  300 W/m2/K
0 5 10 15 20
Distance [km]

30. 24’’ Wet Gas Cooling Section
120
Burial = 0% (OHTC = 508.9 W/m2/K)
110 Burial = 25% (OHTC = 336.4 W/m2/K)
100 Burial = 50% (OHTC = 252.6 W/m2/K)
Burial = 75% (OHTC = 173.3 W/m2/K)
Fluid temperature [°C]
90
Burial = 90% (OHTC = 115.2 W/m2/K)
80
Burial = 99% (OHTC = 50.5 W/m2/K)
70
60
50
40
30
20
10
0
hamb  800 W/m2/K
0 5 10 15 20
Distance [km]

31. 40’’ Trunkline
70
OHTC = 13.1 W/m2/K (Ovuworie)
60 OHTC = 14.8 W/m2/K (Morud & Simonsen)
OHTC = 15.3 W/m2/K (CFD)
Fluid temperature [°C]
50
OHTC = 15.6 W/m2/K (OTC 23033)
40 OHTC = 20.3 W/m2/K (Carslaw & Jaeger)
OHTC = 23.4 W/m2/K (No burial)
30
20
10
Burial = 50%
0
0 20 40 60 80 100 120 140 160 180 200
Distance [km]

32. 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)

33. Mixed Boundary Conditions
At the pipe external surface (r = Dext/2)
y
x
At the ground surface (y = 0)
r

34. Burial Depth
Seabed
H
Dext

35. Ambient Film Coefficient
External heat transfer coefficient
24‐in Wet Gas Cooling Section
1100
1000
hext [W/m2/K]
900
PIPESIM 2009
(current speed 0.1 m/s)
800 CFD (FLUENT)
(current speed 0.1 m/s)
700 PIPESIM 2009
(current speed 0.01 m/s)
CFD (FLUENT)
600 (current speed 0.01 m/s)
500
0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%
Burial [%]

36. 24’’ Wet Gas Cooling Section
Contour plot of temperature [K]
for 50% burial

37. 24’’ Wet Gas Cooling Section
Contour plot of temperature [K]
for 95% burial

38. 42’’ Offshore Trunkline
Contour plot of temperature [°C]
for 50% burial

39. 42’’ Offshore Trunkline
Contour plot of temperature [°C]
for 95% burial