Gas Pipeline I

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.


2/26

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


3/26


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


4/26


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


5/26


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


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


7/26

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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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


9/26


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


10/26


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


11/26

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


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


12/26


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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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.


14/26


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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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


16/26


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


17/26


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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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


19/26


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


20/26


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.


21/26


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


22/26


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


23/26


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


24/26


25/26

16 in., 100 MMSCFD, 80F

roughness of 700 in. for AGA and Colebrook,

pipeline efficiency of 0.95 in Panhandle and Weymouth


26/26

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

Documents

Gas Pipeline I