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8/22/2019 Gas Pipeline I
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Ref.1: Brill & Beggs, Two Phase Flow in Pipes, 6th Edition, 1991.
Chapter 1.
Ref.2: Menon, Gas Pipeline Hydraulic, Taylor & Francis, 2005,
Chapter 2.
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General Flow Equation
Energy balance at steady state:
EnergyPotential:
EnergyKinetic:2
En
ergynCompressioorExpansion:
EnergyInternal:
1
2
1
11
1
c
c
g
Zgm
g
vm
VP
U
c
c
g
Zgmg
vm
VP
U
2
2
2
22
2
2
cc
s
cc g
mgZ
g
mvVPUWq
g
mgZ
g
mvVPU 2
2
2222
1
2
1111
22
fluidon thedoneWorkandfluidthetoaddedHeatWhere
sWq
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General Flow Equation
Dividing by m and writing in differential form:
By using the enthalpy and entropy definition:
0dddd
dd
s
cc
Wq
g
Zg
g
vvPU
P
STh
P
Uh
d
dd,ddd
0ddddd
d scc
Wqg
Zg
g
vvPST
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General Flow Equation
For irreversible process therefore:
For an inclined pipe, therefore:
0d)d(ddd
scc
Wlosses
g
Zg
g
vvP
)(ddd lossesqST
No Work
sindd LZ
L
losses
g
g
Lg
vv
L
P
cc d
)(dsin
d
d
d
d
0:FlowDownFor
0:FlowFor Up
frictionL
P
d
d
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General Flow Equation
Fanning friction factor ( f):
Wall shear stress:
Darcy or Moody friction factor (fm):
c
w
g
vf
2
2
P P+dP
Ld
dPPP
wd)(
4)d(
2
dg
fv
dL
P
c
w
f
224
d
d
dg
vf
L
Pff
c
m
f
m
2d
d4
2
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dgvf
gg
Lgvv
LP
c
m
cc 2sin
dd
dd
2
General Flow Equation
Pressure gradient in pipe:
frictionelevationonacceleratitotal L
P
L
P
L
P
L
P
d
d
d
d
d
d
d
d
Usually negligible Zero for horizontal pipe
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Single Phase Gas Flow
Reynolds Number
Reynolds Number in Gas Pipeline:
)cp(
)/ftlb()ft/sec()ft(
1488
3
mRe
vd
N
g
gg
gggA
qvqAv scsc
scsc
rateflowMass
)in()cp(
)Mscfd(14.20
0764.04
1488
2
Red
qd
qd
Ngg
g
g
gg
sc
sc
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Single Phase Gas Flow
Friction Factor
Laminar Flow (NRe < 2100):
Turbulent Flow (NRe > 2100): Moody Diagram
Smooth Wall Pipe:
Rough Wall Pipe:
Re
64
Nfm
6
Re
332.0
Re 1031035.00056.0 NforNfm
in0006.0:,25.21
log214.11
9.0
Re
10
Commonly
Ndfm
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Single Phase Gas Flow
General Equation
g
gg
c
m
cc d
qv
dg
vf
g
g
Lg
vv
L
Pscsc
2
2 4,
2
sin
d
d
d
d
dg
RTz
PMd
RTMPq
RTz
PMf
g
gRTz
PM
L
P
c
g
g
sc
gsc
g
g
g
m
c
g
g
sc
2
4
sin
d
d
2
2
RPdTg
fTzqMP
RTzg
gPM
L
P
scc
mgggsc
gc
g sc
522
228sin
d
d
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Single Phase Gas Flow
General Equation
sin
8sin
d
d522
2222
2
dgT
fTzqP
PRTzg
gM
L
PP
sc
mavavgsc
avavc
g sc
IfTandzgare constant (T=Tav andzg=zav):
2
sind1
222
S
RTzg
LgM
CP
PPP
Pavavc
g
S
CP
CP
22
2
22
1ln 122221 SS eCPeP
C2
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5.0
522
21
5.052
22
1 6354.594.198
emavavg
s
sc
sc
emavavg
s
gLfTz
dPeP
P
T
LfTz
dPePq
sc
S
eL
d
qTfzPeP
SgavmavgS sc 1(ft)
in)(
Mscfd)(R)(10527.25
2o5
2
2
2
1
Single Phase Gas Flow
General Equation
116
522
22
2
2
2
1 S
csc
gmavavgscS eRSgdT
MLfTzqPPeP sc
Le
)R(
)ft(0375.0o
avav
g
Tz
ZSWhere
LLS
ePipeHorizontalFor
e
S
S
11
lim:0
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Single Phase Gas Flow
Average Pressure
10221 xWherexLKPP x )1(2
2
2 xLKPPx
116
522
22
2
2
2
1 S
csc
gmavavgscS eRSgdT
MLfTzqPPeP sc
5.0
222121
2
2
222
1 )(1 PPxPPx
PP
x
PPxxx
22
2
1
3
2
3
1
21
2
21
1
0
3
2
3
2d
PP
PP
PP
PPPxPP avxav
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Single Phase Gas Flow
Erosional Velocity
Higher velocities will cause erosion of the pipe interior
over a long period of time. The upper limit of the gas
velocity is usually calculated approximately from the
following equation:
)lbm/ft(
100ft/s)(3
max
g
v
Usually, an acceptable operational velocity is 50% of the above.
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Single Phase Gas Flow
Pipeline Efficiency
In Practice, even for single-phase gas flow, some water or
condensate may be present. Some solids may be also
present. Therefore the gas flow rate must be multiply by
an efficiency factor (E).
A pipeline withEgreater than 0.9 is usually considered
clean .
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Single Phase Gas Flow
Non-Iterative EquationsSeveral equations for gas flow have been derived from General
Equation. These equations differ only in friction factor relation
assumed:
Gas Transmission Pipline
1. AGA equation
2. Weymouth equation
3. Panhandle A equation
4. Panhandle B equation
Gas Distribution Pipeline
1. IGT equation
2. Spitzglass equation
3. Mueller equation
4. Fritzsche equation
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Single Phase Gas Flow
AGA EquationThe transmission factor is defined as:
First,Fis calculated for the fully turbulent zone. Next,Fis
calculated based on the smooth pipe law. Finally, the smaller of
the two values of the transmission factor is used.
mfF
2
PipeSmoothF
NF
F
NF
TurbulentFullyd
F
Min
t
t
t
6.0log4,4125.1
log4
7.3log4
Re10
Re10
10
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Single Phase Gas Flow
Weymouth Equation
The Weymouth equation is used for high pressure, high flow
rate, and large diameter gas gathering systems.
The Weymouth friction factor is:
3/1
032.0
dfm
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Single Phase Gas Flow
Panhandle A Equation
The Panhandle A Equation was developed for use in large
diameter natural gas pipelines, incorporating an efficiency factor
for Reynolds numbers in the range of 5 to 11 million. In this
equation, the pipe roughness is not used.
The Panhandle A friction factor is:
1461.0
Re
0768.0
N
fm
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Single Phase Gas Flow
Panhandle B Equation
The Panhandle B Equation is most applicable to large diameter,
high pressure transmission lines. In fully turbulent flow, it is
found to be accurate for values of Reynolds number in the range
of 4 to 40 million.
The Panhandle B friction factor is:
03922.0
Re
00359.0
N
fm
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Single Phase Gas Flow
Gas Transmission Equations
A. Comparison of the calculated Output Pressureby AGA,
Colebrook, Weymouth and Panhandle equations: Figure 2.5
B. Comparison of the calculated Flow rateby AGA, Colebrook,
Weymouth and Panhandle equations: Figure 2.6
We therefore conclude that the most conservative flow equation
that predicts the highest pressure drop is the Weymouth equation
and the least conservative flow equation is Panhandle A.
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Single Phase Gas Flow
IGT Equation
The IGT equation proposed by the Institute of Gas Technology is
also known as the IGT distribution equation:
cp,861.35 667.2555.0
2.08.0
2
2
2
1
d
LT
PeP
P
Tq
eavg
s
sc
scgsc
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Single Phase Gas Flow
Spitzglass EquationThe Spitzglass equation originally was used in fuel gas piping
calculations. This equation has two version
A. Low pressure (less than 1 psig):
B. High pressure (more than 1 psig):
5.2
5.0
21
)03.06.3
1(
956.278 d
dd
LT
PP
P
Tq
eavgsc
scgsc
5.2
5.0
2
2
2
1
)03.06.3
1(
016.53 d
ddLzT
PeP
P
Tq
eavavg
S
sc
scgsc
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Single Phase Gas Flow
Mueller and Fritzsche Equation
The Mueller equation is:
The Fritzsche formula, developed in Germany in 1908, has found
extensive use in compressed air and gas piping:
cp,4509.35 725.2575.0
2609.07391.0
2
2
2
1
d
LTPeP
PTq
eavg
s
sc
scgsc
69.2
538.0
8587.0
2
2
2
128.41 d
LT
PeP
P
Tq
eavg
s
sc
scgsc
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16 in., 100 MMSCFD, 80F
roughness of 700 in. for AGA and Colebrook,
pipeline efficiency of 0.95 in Panhandle and Weymouth
8/22/2019 Gas Pipeline I
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30 in., 100 miles, 80F, output pressure of 800 psig
roughness of 700 in. for AGA and Colebrook,
pipeline efficiency of 0.95 in Panhandle and Weymouth