important aspects of gas temperature modeling in long subsea pipelines
TRANSCRIPT
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PSIG 0901
Important Aspects of Gas Temperature Modeling in Long Subsea Pipelines
J oakim Ramsen, Polytec, Norway (1)Svein-Erik Losnegrd, Polytec, Norway (1)Leif Idar Langelandsvik, Gassco, Norway (2)Are J . Simonsen, Dynavec AS, Norway (3)Willy Postvoll, Gassco, Norway (4)
Copyright 2009, Pipeline Simulation Interest Group
This paper was prepared for presentation at the PSIG Annual Meeting held in Galveston,Texas, May 12 May 15 2009.
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ABSTRACTGassco supplies Norwegian natural gas to the European
market through nearly 5,000 miles of large-diameter high-pressure subsea pipelines. In 2007 3106 MMSCF of gas were
exported from the Norwegian Continental Shelf (NCS).
During the winter, demand for gas usually exceeds theestimated transport capacity of the pipelines. More accurate
modeling of the flow can lead to improved use of available
network capacity.
The pipelines in Gasscos network are typically 200 560miles long, and the gas temperature is only measured at the
inlet and outlet. Consequently, the calculated gas temperature
along the pipeline depends on the accuracy of the assumedambient temperature and the estimated heat transfer. This
paper mainly focuses on heat transfer modeling, and how this
affects the estimated gas temperature. The importance of a
correct total heat transfer coefficient for different conditions
has been studied, and the most important parametersassociated with this coefficient have been identified. A
recommendation regarding which parameters to focus on
under different conditions such as different burial depths and
flow rates is given.
INTRODUCTIONThe Norwegian gas is transported in seven large diameter sub-
sea pipelines to United Kingdom and continental Europe,
covering around 15 % of the European natural gas
consumption. The transportation network is operated by thestate-owned company Gassco.
The Norwegian export pipelines are between 200 and 560
miles long, and have diameters up to 44 inches. Pressure
transmitters, flow meters and temperature measurements are
only located at the inlet and at the outlet. To know the state of
the gas between those two points one has to rely solely oncomputer models and simulators, which are very important in
order to obtain optimal operation of the pipelines. The
computer models are used for general monitoring of the gastransport, providing estimated arrival times for possibly
unwanted quality disturbances and pigs, predictive
simulations when the operational conditions changes and for
transport capacity calculations. The transport capacity is
usually made available to the shippers of the gas many yearsin advance, and accurate calculations early in a pipelines
lifetime are appreciated and valuable.
High accuracy in the transport capacity calculations isimportant to ensure optimal utilization of invested capital in
the pipeline infrastructure. The calculations need to be as close
to, but not higher than, the true capacity as possible. This wil
ensure optimal utilization of invested capital. As soon as apipeline is built, the true capacity is determined by the
diameter, length, available inlet compression, gas temperature
and other physical parameters. A lot of effort is put in to
estimate this capacity figure exactly.
In 2004 a research program was launched to optimize the gas
transport modeling involving high flow rates, high pressures
large diameters and very low roughnesses. The R&DFoundation Polytec and Gassco have worked together for
several years to optimize the gas transport modeling. In the
project several subtasks have been conducted or are ongoing
to improve the friction factor correlation, viscosity
measurements and implement new viscosity correlation, use of
more accurate ambient temperatures and more accuratemodeling of heat transfer. This paper will focus on work
performed related to heat transfer.
After realising that the simulation tool used in the project did
not model the heat transfer for partially buried pipelines, a
literature survey was conducted to identify an appropriate
model. It seems that very few published articles discuss thistopic [1, 2]. An analytical model [1] was identified, able to
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2 J . RAMSEN, S-E. LOSNEGRD PSIG 090
calculate the heat transfer for partially buried pipelines. This
model, which has been evaluated by CFD simulations, hasbeen used to calculate the gas temperature in partially buried
pipelines.
This paper starts with a system description, followed by a
theory section about heat transfer including the most important
equations used in pipeline gas temperature modeling. Then,the parameters determining the total heat transfer coefficient
are studied. Also, the gas temperature responses for relevanttotal heat transfer coefficients are given. These responses are
used to discuss the accuracy of gas temperature modeling and
in particular the modeling of partially buried pipelines.
Mainly, a constant ambient temperature profile is applied, but
a scenario where the ambient temperature is increased over a
short distance is also looked into. Only gas temperaturemodeling in connection with steady-state simulation is
considered.
SYSTEM DESCRIPTION
Typical characteristics of the Gassco operated pipelines:Pressure range: 700 3,000 psi
Diameter: 30 45 inches
Composition: 80 95 % MethaneLength: 200 560 miles
Flow rate: 700 2,120 MMSCF/d
Roughness: ~104 inches, due to internal
coating
Location: Sea bed (Mostly partially buried)Sea depth: 150 100 ft
Metering: Pressure, temperature, flow and
composition at inlet and outlet
Pipe materials: Steel, Asphalt Enamel and
ConcreteTotal export 2007: 3106 MMSCF
Figure 1: Typical pipeline cross section consisting of a steelpipe coated with ashphalt enamel and concrete
Theory
The general heat transfer equation
The general heat transfer equation used by pipeline simulation
software is given by Equation 1.
( )gasamb TTAUQ =& Equation 1
Where
Q& Heat transferred between the gas and the
surrounding medium [Btu/h]
U Overall heat transfer coefficient [Btu/hftF]
A Surface area of the pipe [ft]
ambT Ambient temperature [F]
gasT Gas temperature [F]
The total heat transfer coefficient, U, describes the conductive
and convective heat transfer between the gas and the
surroundings.
Heat transfer with multiple wall layers
Long subsea pipelines are usually coated with asphalt ename
and concrete for corrosion protection and bouancystabilization. Thus, the thermal energy must pass through
several shells to enter/exit the pipe. Assuming pure radial
flow, these multiple resistances may be combined into a single
heat transfer coefficient as shown inEquation 2.
1
2 1
1ln
1
=
+
+=
N
n on
n
n
o
ii
o
hr
r
k
r
hr
rU Equation 2
Where
U Overall heat transfer coefficient of a pipe with
outer radius [Btu/hftF]or
ir Inner radius of pipe [ft]
or Outer radius of pipe [ft]
nr Outer radius of wall layer [ft]n
nk Conductivity of wall layer [Btu/hftF]n
ih Inside heat transfer coefficient [Btu/hftF]
oh Outside heat transfer coefficient [Btu/hftF]
The outer film coefficient has to be determined according to
the surroundings of the pipeline.
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Fully exposed pipelines
For pipelines fully exposed to water the convective heat
transfer is given by Equation 4, where the Nusselt number canbe obtained from Equation 3. The latter equation yields for
external flow across a cylinder for Reynolds numbers
exceeding 200. This corresponds to velocities greater than
310-4 ft/s, for typical sea water properties and pipeline
diameter.
3.06.0 PrRe26.0 =Nu Equation 3
Where
Nu Nusselt number
Re Reynolds number
Pr Prandtl number
The Nusselt number can then be used to calculate the outside
heat transfer coefficient.
o
seao
d
kNuh
= Equation 4
Where
Thermal conductivity of sea water [Btu/hftF]seak
Outer diameter [ft]od
Buried pipelines
For buried pipelines the outside heat transfer coefficient is
given by Equation 5.
( )1ln
2
2 +=
xx
dk
h osoil
o Equation 5
Where
soilk Thermal conductivity of the soil [Btu/hftF]
x od
H2=
H Distance from center of pipeline to sea floor [ft]
Partially buried pipelines
An analytical model has been used to model the heat transferin partially buried pipelines. This model was developed by
J. C. Morud [1]. It is described by Equation 6, from which Usea
is given by combining Equation 2 and Equation 4 and Uground
is given by Equation 7. Figure 6 illustrates how the burial
depth is defined.
groundb
seab
total UUU
+=
1 Equation 6
Where
Overall heat transfer coefficient [Btu/hftF]totalU
b
=
R
Harccos
R Outer radius of pipeline [ft]
seaU Combination of and convective heat
transfer to the sea water [Btu/hftF]
wallU
groundU Combination of and conductive heat
transfer to the soil [Btu/hftF]
wallU
( )
( )
0 for the base case.
The low conductivity case resulted in quite low U-values for
the whole burial span. Hence, for pipelines with a low U-value
the importance of using correct burial depths increases. Figure
12 shows the gas temperature profiles for this case. It is shown
that the gas temperature profile is more sensitive to changes inburial depth when the pipeline is more than half buried
(H/R>0).
Recovery length
Incorrect heat transfer modeling in the first part of the pipeline
can be disguised if a sufficient length of the last part iscorrectly modelled. In this paper that length is called the
recovery length, and a sensitivity study was carried out to see
how long this is for different U-values.
In the sensitivity study recovery length is the length required
to correct an error of 3.6 F in the calculated gas temperature
compared to the real gas temperature. It is assumed that Teq for
each U-value is equal to the correct gas temperature.
The gas temperature is set to be 3.6 F lower at distance 0.Then the recovery length is found when the gas temperature is
within -0.36 F from the real gas temperature (Teq), see Figure
13. Note that an isothermal ambient temperature profile is
used in the analysis.
The results from the analysis are shown in Table 8. It can be
seen that the recovery length decreases significantly withincreasing U-values. Thus, for pipelines with high U-values in
the last part, correct modeling of this part is more likely to
disguise errors in the heat transfer modeling of the first part
This can make it difficult to tune the model according to thetemperature reading at the outlet.
Table 8: Recovery length for different U-values at high flow
U-value[Btu/hftF]
Recovery Length[miles]
0.49 261
1.25 103
1.69 76
3.13 41
The U-values in a typical pipeline operated by Gassco are
plotted in Figure 14. It is shown that the U-values for the last
60 miles, range from 0.28 0.32 Btu/hftF. This is because
this part usually is fully buried. In zone A and B, however, thepipeline is partially buried or fully exposed. Hence, error
made in zone C will give a temperature deviation at the outlet
while errors made in zone A and B can be disguised.
TEMPERATURE TUNING
If there is a discrepancy between the modeled and measured
outlet temperature in a pipeline it is common to tune the
model, either by adjusting heat transfer or the ambient
temperature. From the observations made in this article the
following can be related to tuning.
For high flows (>16 ft/s):
If the U-values are high (>1.76 Btu/hftF) for themain part of the pipeline, the accuracy of calculatedgas temperature will depend strongly on the accuracy
of the ambient temperature. Thus, if the modeled
outlet temperature deviates significantly from the
measured temperature this is most likely due to anerror in the imposed ambient temperature profile.
For low U-values (
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8 J . RAMSEN, S-E. LOSNEGRD PSIG 090
large pipelines leading to Europe. The U-values that were
tuned with these data, see Figure 15, are called Utuned, andrepresent the actual U-values of the pipeline.
Figure 5: The pig prior to launching at Krst gas processingplant. The pig launcher is seen in the background.
In todays model the pipeline will be assumed either fully
exposed or totally buried based on best available data. In this
analysis U is set to 0.7 Btu/hftF when H/R>0 and
correlation for fully exposed pipeline is used when H/R
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error of 0.18 Btu/hftF can lead to an error of more
than 3.6 F in the calculated gas temperature.
Even though the calculated outlet temperature equalsthe measured one this does not necessarily verify the
model. If a part of the pipeline has a high U-value
(>1.76 Btu/hftF), a correct modeling of this part
may disguise errors in the model upstream.
The Morud model for partially buried pipelinesagrees well (within 10%) with CFD calculations. At
high Biot numbers (>102) the deviation increases,
especially for buried pipelines. Subsea pipelinesusually have a Biot number below 10.
REFERENCES1. J. C. Morud and A. Simonsen, Heat transfer from
partially buried pipes, 16th Australasian Fluid Mechanics
Conference December 2007
2. Alessandro Terenzi and Francesco Terra, External heatransfer coefficient of a partially sunken sealine, IntComm. Heat Mass Transfer. Vol. 28. No. 2, pp 171-179
2001
3. M. Mohitpur, H. Golshan and A. Murray, Pipeline Designand Construction A Practical Approach, p. 106-110
4. Leif Idar Langelandsvik, Modeling of natural gas
transport and friction factor for large scale pipelines Laboratory experiments and analysis of operational data
20085. Martin Mathiesen,North sea bottom temperature, Polytec
R&D Foundation June 2004
ACKNOWLEDGEMENTSThe Norwegian Research Council is acknowledged for the
funding provided for the PhD-work in this research project.
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TABLES
Table 9: A sensitivity study on the properties of the pipeline and its surroundings. The sensitivities are tabulated as difference from thethe base case (sensitivity base case)
Value Utotal
Case DescriptionFrom To
FullyExpose H/R = -0.75 H/R = 0 H/R = 0.75
TotallyBuried
Base case Base case--- --- =3.1 =2.6 =1.9 =1.2 =0.5
Sensitivity 1 3.5 5.2 +1.1 +0.9 +0.6 +0.3 +0.0
Sensitivity 2
Change in concrete
conductivity3.5 1.7 -1.4 -1.1 -0.7 -0.4 -0.1
Sensitivity 3 1.2 1.7 +0.1 +0.1 +0.1 0.0 0.0
Sensitivity 4
Change in asphalt
conductivity1.2 0.7 -0.3 -0.2 -0.2 -0.1 0.0
Sensitivity 5 86.5 103.8 0.0 0.0 0.0 0.0 0.0
Sensitivity 6
Change in steel conductivity
86.5 69.2 0.0 0.0 0.0 0.0 0.0Sensitivity 7 4.2 5.4 -0.5 -0.4 -0.3 -0.2 0.0
Sensitivity 8
Change in concretethickness
4.2 2.9 +0.7 +0.6 +0.4 +0.2 0.0
Sensitivity 9 0.3 0.3 -0.1 -0.1 0.0 0.0 0.0
Sensitivity 10Change in asphalt thickness
0.3 0.2 +0.1 +0.1 0.0 0.0 0.0
Sensitivity 11 1.1 1.3 0.0 0.0 0.0 0.0 0.0
Sensitivity 12Change in steel thickness
1.1 1.0 0.0 0.0 0.0 0.0 0.0
Sensitivity 13 0.3 0.5 0.0 0.0 0.0 0.0 0.0
Sensitivity 14
Change in velocity of sea
current0.3 0.2 -0.1 -0.1 -0.1 0.0 0.0
Sensitivity 15 3.5 5.2 0.0 +0.1 +0.1 +0.1 +0.2
Sensitivity 16
Change in ground
conductivity3.5 1.7 0.0 -0.1 -0.1 -0.2 -0.2
Sensitivity 17 Ignoring hi 52.8 0.0 0.0 0.0 0.0 0.0 0.0
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FIGURES
Figure 6: Definition of coordinates for partially buried pipelines
Figure 7: Qualitative description of gas temperature profiles
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12 J . RAMSEN, S-E. LOSNEGRD PSIG 090
40.0
40.5
41.0
41.5
0 50 100 150 200 250 300
Distance [m i]
Tem
perature[F]
Tamb
Case 1
Case 2
Figure 8: Gas temperature responses for low flow and low pressure drop situations
30.0
35.0
40.0
45.0
0 50 100 150 200 250 300
Distance [m i]
Tem
perature[F]
Tamb
Case 3
Case 4
Figure 9: Gas temperature response for high flow and high pressure drop situations
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PSIG 0901 Important Aspects of Gas Temperature Modeling in Long Subsea Pipelines 13
30.0
35.0
40.0
45.0
0 50 100 150 200 250 300
Distance [m i]
Tem
perature[F
]
Tamb
Case 5
Case 6
Figure 10: Gas temperature response when the ambient temperature increase by 2 C over a short distance
0
2
4
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5 3
U-value
Tamb-Teq
[F]
High Flow
Low Flow
Figure 11: Difference between Tamb and Teq versus U-value
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25.0
30.0
35.0
40.0
45.0
0 50 100 150 200 250 300
Distance [m i]
Tem
perature[F]
Tamb
Fully exposed
H/R = -0.75
H/R = 0
H/R = 0.75
Totally buried
Figure 12: Gas temperature profiles including partially buried pipelines (Low conductivity case)
Figure 13: Illustration of recovery length
T = 0.36 F
At this point the simulatedgas temperature is 3.6 F
below the real gas
temperature.Recovery Length
Assumed that U is correct for this part
Temperature
Ambient temperature
Real gas temperature / Teq
Simulated gas temperatureGas temperature response
Distance
When gas temperature is 0.36 F from thereal gas temperature the recovery length is
found.
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PSIG 0901 Important Aspects of Gas Temperature Modeling in Long Subsea Pipelines 15
0
1
2
3
4
5
6
0 50 100 150 200 250 300 350 400 450
Length [mi]
U-value[Btu/ftFh]
Figure 14: U-values in a typical Gassco operated pipeline
0
1
2
3
4
5
6
10
50
90
130
170
210
250
mi
U-value[Btu/ftF
h]
U_tuned U_as_today U_pbur U_pbur_high_conductivity
Figure 15: Comparison of 4 sets of U-values
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43.5
44.5
45.5
46.5
47.5
48.5
49.5
45 90 135 180 225 270
m i
Tem
perature[F]
U_ tuned Partial buried model As_ Today PBur high cond.
Figure 16: Temperature profiles based on simulation with different U-value sets.
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Authors
Joakim Ramsen is a researcher at the R&D foundationPolytec located in Haugesund, Norway. He started his
professional career in 2003 and has worked mainly with
projects concerning gas transport modeling. Since 2005 he hasbeen the project leader for a project called optimized flow
modeling. In addition he has been involved in several CO2transport simulations projects conducted in Norway.
Svein-Erik Losnegrd is a researcher at Polytec R&DFoundation. He holds a MSc. Degree in Mechanical
engineering from NTNU (2006). His work has mainly been
concerned with gas transport modeling.
Leif Idar Langelandsvik is a principal engineer with Gassco,Technology Department. He is about to finish up a PhD
degree at the Norwegian University of Science and
Technology (NTNU) with focus on modeling of gas transport
in full scale pipelines at large Reynolds numbers. Particularfocus is on the wall friction at such conditions. The work at
Gassco is mainly focused on improving gas transport models,pipeline simulations, fluid dynamics and transport capacitycalculations. He received his MSc. degree in
cybernetics/control systems at NTNU in 1999.
Are Simonsen is currently project manager in Dynavec AS.He holds a PhD. in fluidmechanics from the University ofTrondheim, NTNU(2003). The last years he has worked with
fluidmechanics, heat-, and mass transfer related problems as a
researcher in SINTEF Materials&Chemistry.
Willy Postvoll is the Real Time Systems Advisor in GasscoAS. He holds a MSc degree in Petroleum and Reservoir
Engineering from the University of Stavanger (1985). Hestarted his professional career with Statoil in 1985 where he
worked as a Reservoir Engineer in the Oil and Gas Field
Development division. After spending 5 years as a Senior
Engineer providing technical support for reservoir simulation
he joined the Transport Division specializing in Real-TimeSystems, Transport Control and Supervision.