otc 23033
DESCRIPTION
The mechanism of steady-state heat transfer from deeply buried pipes has been rigorously modeled for a long time. Detailed analytical formulae have been proposed recently for the calculation of the overall heat transfer coefficient across the entire range of burial depths. This paper presents an evaluation of these formulae and suggests some improvements on the basis of numerical simulations performed with high-fidelity Computational Fluid Dynamics (CFD) models. Explicit formulae can quickly be implemented and used for generating profiles of overall heat transfer coefficient along pipelines. The effect of uncertainties in input data on steady-state heat transfer can easily be assessed for any amount of burial. Four explicit, continuous formulae are presented and compared to three independent sources of CFD analyses. A relative difference of 10% or less with respect to CFD can be achieved with analytical formulae for a comprehensive range of offshore pipeline systems, ambient conditions, soil thermal conductivities, and burial depths. The applicability of these formulae to onshore systems is also evaluated.TRANSCRIPT
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 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
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-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
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 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
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%
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
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
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
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
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
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
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]
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
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
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 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
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%
OH
TC [W
/m2/
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)
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%
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
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
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%
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/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)
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
42’’ Offshore TrunklineContour plot of temperature [°C]
for 50% burial
42’’ Offshore TrunklineContour plot of temperature [°C]
for 95% burial