otc 23033 presentation

OTC 23033A Holistic Approach to Steady-State Heat Transfer

from Partially and Fully Buried Pipelines

Erich Zakarian

James Holbeach

Julie Morgan

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

Reduced heat loss from high temperature fluids• Hotter temperature profiles for longer Uncontrolled pipeline lateral buckling

• Under design of cooling spoolsAccelerated 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

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

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]

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)

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)

Typical Pipe Wall U‐values

Transport systemTypical 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

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]

Holistic Approach

Transport systemTypical

pipe Biot number [‐] Pipe‐in‐pipe system Highly insulated pipeline Flexible flowline

Up to 4


4 to 50


Above 50

0

2

4

6

8

10

12

0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%

OHTC

[W/m

2/K]

Burial depth [%]

OHTC vs. Burial Depth

0%

100%

200%

50%



Up to 4


4 to 50


Above 50

Low Pipe Biot Number

0

2

4

6

8

10

12

0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%

OHTC

[W/m

2/K]

Burial depth [%]

Carslaw & Jaeger

Morud & Simonsen

Ovuworie

OTC 23033

CFD (CFX 12.1)

14’’ Insulated Pipeline

Bip= 2.1

10% error bar

Intermediate Pipe Biot Number



Up to 4


4 to 50


Above 50

0

5

10

15

20

25

30

0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%

OHTC

[W/m

2/K]

Burial [%]

Carslaw & Jaeger

Morud & Simonsen

Ovuworie

OTC 23033

CFD (FLUENT 6.2)

40’’ Trunkline

Bip= 4.2

10% error bar

High Pipe Biot Number



Up to 4


4 to 50


Above 50

0

100

200

300

400

500

600

0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%

OHTC

[W/m

2/K]

Burial [%]

Carslaw & Jaeger

Morud & Simonsen

Ovuworie

OTC 23033

CFD (FLUENT 13.0)

24’’ Wet Gas Cooling Section

Bip= 441.2

10% error bar

And what about onshore pipelines?

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]

EnvironmentTypical ambient fluid film coef. [W/m2/K]

Typical groundBiot number [‐]

Onshore 4 to 30 Up to 15

Offshore 200 to 1000+ Above 50

0

2

4

6

8

10

12

14

16

18

0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%

OHTC

[W/m

2/K]

Burial [%]

Carslaw & Jaeger

Morud & Simonsen

Morud & Simonsen (original)

Ovuworie

OTC 23033

40’’ Onshore Trunkline

Bip= 17.3Big= 2.3

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

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

Recommended FormulaeTransport system Environment

Recommendedformulae

Pipe‐in‐pipe system Highly insulated pipeline Flexible flowline

Offshore • Morud & Simonsen• OTC 23033Onshore


Offshore • Morud & Simonsen• OTC 23033

Onshore • Ovuworie• OTC 23033


Offshore• Morud & Simonsen• Ovuworie• OTC 23033

Onshore • Ovuworie• OTC 23033

OTC 23033A Holistic Approach to Steady‐State Heat Transfer from

Partially and Fully Buried Pipelines

Erich Zakarian

James Holbeach

Julie Morgan

0

2

4

6

8

10

12

14

16

18

0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200%

OHTC

[W/m

2/K]

Burial [%]

Carslaw & Jaeger

Morud & Simonsen

Ovuworie

OTC 23033

CFD (FLUENT 13.0)

Bip= 9.5

42’’ Offshore Trunkline

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)

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)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

0 10 20 30 40 50 60 70 80 90 100

Fluid tempe

rature [°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%

0

10

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20

Fluid tempe

rature [°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)


hamb 300 W/m2/K

0

10

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20

Fluid tempe

rature [°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)


hamb 800 W/m2/K

0

10

20

30

40

50

60

70

0 20 40 60 80 100 120 140 160 180 200

Fluid tempe

rature [°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%

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)

r

At the pipe external surface (r = Dext/2)

At the ground surface (y = 0)

Mixed Boundary Conditions

y

x

Burial Depth

H

Seabed

Dext

Ambient Film Coefficient

500

600

700

800

900

1000

1100

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%

h ext[W

/m2/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)

24’’ Wet Gas Cooling Section Contour plot of temperature [K]

for 50% burial

24’’ Wet Gas Cooling Section Contour plot of temperature [K]

for 95% burial


Contour plot of temperature [°C] for 50% burial


Contour plot of temperature [°C] for 95% burial

otc 23033 presentation

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