PRESSURE DROP IN GAS
PIPELINES AND WELLS
Jón Steinar Guðmundsson
TPG4140 Natural Gas
September 12, 2012
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Importance of pressure drop and different pipes
Pressure drop in pipelines (depends on d5)
Equations for liquid and gas flow
North Sea gas pipelines
Friction factor and roughness
R&D on friction (roughness) and pressure drop
Summary
A: Wells, B: Flowlines, C: Risers, D: Process pipes, E: Off-Loading, F: Pipelines
Importance of pressure drop
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Transport capacity, we want to be able to push as much gas as
possible through existing pipelines to customers. Norwegian export
pipelines >100 BCM annually.
Expensive gas compression (power and emissions) needed to give
sufficient inlet pressure to overcome pressure drop. Gas turbines
drive large centrifugal compressors offshore. Largest consumption
of power offshore. Gas turbines and electrical motors on land.
Export pipelines have epoxy coating to make wall smoother to
reduce wall friction and hence greater flow capacity.
Production capacity (subsea-to-beach), we want to maintain
wellhead pressure as low as possible to sustain large production
rate from gas fields with time. Eventually we need subsea
compression.
Large diameter pipelines used to avoid compression platforms along
export gas pipelines. On land, compressor stations along pipeline.
Natural Gas Pipelines
• We have pipelines on land for long-distance transport
and regional distribution.
• We have buried pipelines for local distribution, to
factories, businesses and homes.
• We have pipes in processing plants, offshore and
onshore.
• We have subsea pipelines within field developments
(flowlines).
• We have large-diameter, long-distance subsea pipelines
from natural gas provinces to market.
• Pipelines are as important an infrastructure as roads,
electricity masts, water pipelines, sewer pipelines etc.
Natural Gas Pipeline
Temperature in Pipelines
Temperature in Pipelines
q  UATLMTD
q  m C p (T1  T2 )
TLMTD
(T1  T )  (T2  T )

T1  T
ln
T2  T
T = Constant = Sea Temperature
A  d (L)
TLMTD 
T1  T2
T1  T
ln
T2  T
(T1  T2 )
m C p (T1  T2 )  Ud ( L)
T T
ln 1
T2  T
  Ud
T2  T  (T1  T ) exp 
 mC p

L

Temperature and Distance
Temperature in Pipelines
 Ud 
L
T2  T  (T1 T ) exp
 mCp 
Insulated pipeline on seafloor: 1 < U (W/m2.K) < 2
Non-insulated pipeline on seafloor: 15 < U (W/m2.K) < 25
Pressure and Temperature With Distance
Åsgard Transport (69.4 vs. 76.9 MSm³/d)
Booster_press
Temperature
Booster_temp
210
50
200
190
45
40
180
35
170
160
30
25
150
20
140
15
130
120
10
5
110
0
200
400
600
Temperature (°C)
Pressure (barg)
Pressure
0
800
Distance KP (km)
Booster compressor duty: 15.5 MW (most likely roughness)
Aamodt (2006)
Effect of Roughness on Hydraulic Capacity and
Outlet Pressure and Temperature
Aamodt (2006)
Pressure Drop in Pipelines
The total pressure drop in pipelines and wells consists of three terms
p  p g   p a  p f
where g (gravitation), a and f stand for hydrostatic, acceleration and
friction, respectively. The three terms can be expressed as
p g  g sin L
pa  uu
p f 
f 1 2
u L
2d
The angel α is measured from horizontal and the lenght is the pipe
lenght, not height over/under the surface. The pressure drop due to
friction is the Darcy-Weisbach equation.
Darcy-Weisbach Equation
Darcy-Weisbach Equation
Liquid Flow and When Gas Average Density Used
pr  2rL
2
r p

2 L
1
2
  f u
8
r p 1
2
 f u
2 L 8
f L 2
p 
u
2 d
Darcy-Weisbach Equation
Force balance, steady-state pipe flow
dpr 2  2rdL w
r dp
w 
2 dL
w 
f L 2
p f 
u
2d
1
fu 2
8
r dp 1
 f u 2
2 dL 8
North Sea Pipelines
Sletfjerding, E. (1999): Friction Factor in Smooth and Rough Gas Pipelines, Dr.Ing.,
Petroleum, NTNU.
North Sea Pipelines
Sletfjerding, E. (1999): Friction Factor in Smooth and Rough Gas Pipelines, Dr.Ing.,
Petroleum, NTNU.
North Sea Pipelines
Sletfjerding, E. (1999): Friction Factor in Smooth and Rough Gas Pipelines, Dr.Ing.,
Petroleum, NTNU.
Composition of Processed Gas
Molecule
Troll (1)
Norway
Sleipner (2)
Norway
Draugen (3)
Norway
Groningen (4)
Netherlands
Methane
Ethane
Propane
Iso-Butane
N-Butane
C5++
Nitrogen
Carbon-dioxide
93.070
3.720
0.582
0.346
0.083
0.203
1.657
0.319
83.465
8.653
3.004
0.250
0.327
0.105
0.745
3.429
44.659
13.64
22.825
4.875
9.466
3.078
0.738
0.720
81.29
2.87
0.38
0,15
0.04
0.06
14.32
0.89
100
100
100
100
(1) After processing at Kollsnes (on-shore processing plant), average for November 2000.
(2) After off-shore processing into off-shore pipelines, combination of Sleipner East and West, average November 2000.
(3) After off-shore processing into pipeline Åsgard Transport to Kårstø (on–shore processing plant) for further processing, average for December 2000.
(4) Into onshore grid in The Netherlands.
Kilde: K. Jakobsen, A/S Norske Shell
North Sea Pipelines: Pressure Gradient
p1
p2
L
(p1-p2)/L
m
bar
bar
km
bar/100 km
kg/s
A
108,42
85,59
812,4
2,81
205,50
B
166,26
145,59
303,5
6,81
383,50
C
107,97
94,16
619,0
2,23
185,40
D
65,22
63,64
48,5
3,26
185,40
E
129,85
86,8
619,0
6,95
334,10
F
72,03
67,45
48,5
9,44
334,10
G
136,3
112,1
227,0
10,66
167,60
H
146,7
95,5
812,8
6,30
348,40
6,06
Sletfjerding, E. (1999): Friction Factor in Smooth and Rough Gas Pipelines, Dr.Ing.,
Petroleum, NTNU.
Pressure Gradient in Gas Pipelines
Gradient (bar/100 km)
North Sea, Sletfjerding
(1999)
Canada, Hughes (1993)*
* Mokhatab o.a. (2006, s. 419)
6 (average 8 pipelines)
15-25
Maximum Gas Velocity*
Sletfjerdings (1999) North Sea Pipelines A-H, uaverage (m/s), only 10-20 % av NORSOK umaximum
*NORSOK P-001 (1999)
Pressure Drop Horizontal Gas Pipeline
dA M
d p 
2
2


p

p

ln
L0
2
1
2


fm zRT
f p 
2


2
2
2
1
Variable and Units
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d = Diameter [m]
A = Cross sectional area [m2]
M = Molecular weight [kg/kmol]
f = Friction factor [-]
m = Mass flow rate [kg/s]
z = Compressibility factor [-]
R = Universal gas constant = 8314 [J/kmol.K]
T = Temperature [K]
p1 = Inlet pressure [Pa]
p2 = Outlet pressure [Pa]
L = Pipeline length [m]
Frictional Pressure Drop Gas Pipeline
Horizontal Pipeline (Oil and Gas)
Inclined Gas Well or Pipeline
f L 2
p f 
u
2d
d A2 M
d  p 22 
2
2
p 2  p1  ln 2   L  0
2
f  p1 
f m z RT
p 22  p12 exp 2ag sin L  
M
a
zRT


b
1  exp2ag sin L 
2
a g sin 
fm 2
b
2 A2 d
Friction Factor in Pipelines
Nikuradse’s Sand-Grain Data
Moody Chart
Add reference to fluid mechanics text book.
Blasius’ Equation
Hydraulically Smooth Pipes
0.316
f  0.25
Re
Re < 100,000
Haaland’s Equation
1
1,8  6,9   k 
  log   

f
n
 Re   3,75d 
n
n  3 for gass
n  1 for væske
1,11n



Wall Roughness in Pipes
Material
Average
Absolut
Roughness
(inch)
Average
Absolut
Roughness
(µm)
Internally plastic coated pipeline
Honed bare carbon steel
Electropolished bare 13Cr
Cement lining
Bare carbon steel
Fiberglass lining
Bare 13Cr
0.200×10-3
0.492×10-3
1.18×10-3
1.30×10-3
1.38×10-3
1.50×10-3
2.10×10-3
5.1
12.5
30.0
33.0
35.1
38.1
53.3
Farshad og Rieke, JPT, oktober 2005, side 82-86.
Blasius, Colebrook-White and Haaland
0,316
f  0, 25
Re
 2,51
1
k 

 2 log

 Re f 3,7 d 
f


1,11n
n

1  1,8
 6,9   k  

log 
 
 
f
n
 Re   3,75d  
Haaland n=1 for liquids, same as Coolebrook-White
Haaland n=3 for gases, same as AGA data
Haaland Friction Factor
Gases, n=3, Hydraulically smooth and k/d=0.001
0,03500
0,03000
Frictionfaktor
0,02500
0,02000
0,01500
0,01000
0,00500
0,00000
0
200000
400000
600000
800000
1000000
1200000
Reynolds-tall
Haaland for gas based on AGA data, lower than for liquids, transition different
Haaland Friction Factor
Liquid n=1 and gas n=3, k/d=0.001
0,03500
0,03000
Friksjonsfaktor
0,02500
0,02000
0,01500
0,01000
0,00500
0,00000
0
200000
400000
600000
Reynolds-tall
Gas 3.8 % lower than liquid at Re=106
800000
1000000
1200000
Nikuradse’s Sand Grain and Real Roughness
Sletfjerding
Ra = Arithmetic mean roughness
Rq = Root-mean-square roughness
Rz = Mean peak-to-valley roughness
Pipes Used by Sletfjerding (Amsterdam 2001)
Sand-grain roughness ks, Measured roughness Rq , Hurste exponent H
4.5 < (ks/Rq) < 5.8
Sand-grain roughness estimate based on Nikuradse’s friction factor equation
Summary
– Equation for pressure drop in horizontal gas pipelines; the
natural logarithm term can often be neglected (because of
gentle decrease in pressure in long pipelines)
– Blasius’s equation used for smooth pipes and when Re<105
while Haaland’s equation is general and includes the effect of
roughness (recommended).
– Pressure drop in gas pipelines lower than in liquid pipelines.
Indicates that semi-empirical correlations are not perfect.
– Friction factor equations conservative, give 5-10 % higher
friction factor and greater pressure drop than measured.
– Friction correlations have come into focus after EOS (gas
density) and gas viscosity correlations have improved.
– Pressure drop in gas export pipelines (up to 1 m in diameter
and 400-1200 km long) is of great economic importance for
Norway as natural gas exporter.