Unit-4 Gas Flow Fundamentals

7/27/2019 Unit-4 Gas Flow Fundamentals

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UNIT-5

GASFLOWFUNDAMENTALS1


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FLOWEQUATION

Flow of natural gas and accompanying liquidsthrough gathering systems, process equipment andtransmission pipelines requires pressure drop as thedriving force.

All fluid flow equations are derived from a basicenergy balance which for a steady state system canbe given as:

Change in internal energy + change in kinetic energychange in potential energy+workdone on the fluid

+ heat energy added to the fluidshaft work done byfluid on surroundings = 0. ----------- (1)

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dU + dv2/2gc+ g/gcdz + d(pv)+ dQ-dws=0 --- (2)

U= internal energy ft-lb f/lbm

v= fluid velocity, ft/sec

z= elevation above a given datum plane , ft

p= pressure , lbf/ft2

V= volume of a unit mass of the fluid,ft

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/lbmQ= heat energy added to the fluid ft-lbf/lbm

ws= shaft work done by the fluid on the surroundings.

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Equation (2) can be converted to a mechanical energybalance using the following thermodynamic relations:

du + d(pv) = dh = Tds + Vdp ---------(3)

h= specific fluid enthalpy, ft-lbf/lbmT= temperature ,oR

s= specific fluid entropy, ft-lbf/lbmnow equation (2) becomes

Tds + Vdp + dv2/2gc+ g/gcdz + dQ -dws=0 ---------(4)For an ideal process ds=-dQ/T ----------(5)

Since no process is ideal

ds -dQ/T -----------(6)

Tds = -dQ + dlw ------ --------(7)lw= lost work due to irreversibilities due to friction.

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On further substitution to equation (4)

-dQ + dlw+ Vdp + dv2/2gc+ g/gcdz + dQ -dws=0(8)

Neglecting the shaft work wsand multiplying throughout

by density

dp + dv2/2gc+ g/gc dz + dlw=0 ---------- (9 )

And it can also be written as

p + v2/2gc+ g/g

c z + p

f=0 --------(10)

pfpressure drop due to friction= fv2l /2gcd

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FRICTIONINPIPE

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The term lwrepresents all energy losses resulting from

Irreversibilities of the flowing stream.

Friction lossesInternal losses due to viscosity effects

Losses due to roughness of the wall of the pipe


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FRICTIONFACTOR

Friction factor f,defined as the ratio of the wallshear stress and the kinetic energy per unitvolume and is used in computing the magnitudeof the pressure drop due to friction.

f=w/(v2

/2gc)For steady state flow in a uniform circular conduit

such as pipe this results in well known Fanningequation: pf= 2fLv

2/gc d

d is the inside pipe diameter.Friction factor f is called the Fanning frictionfactor.

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Usually , the moody friction factor equal to 4f is used.

In terms of the Moody friction factor f, the Fanning

equation becomes: pf= fL v2/2gc d

Moody friction factor is therefore a function of Reynolds

number and relative roughness.

f=f(NRe,//d)

hfs=4fLv2/2gcd

Head loss in terms of height of liquid flowing

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REYNOLDSNUMBER

It is named after Osborne Reynolds

(1842-1912), who proposed it in

1883.

= Inertia forces /viscous forces

NRe= dv/

d= inside diameter of the conduit through which the fluid is

moving

v= velocity of the fluid =density of the fluid

=viscosity of the fluid
http://en.wikipedia.org/wiki/Image:Oreynolds.jpg


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Thus, it is used to identify different flow regimes, such as

laminar or turbulent flow.

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Laminar flow

Re < 2000

'low' velocity

Dye does not mix with water

Fluid particles move in straight lines

Simple mathematical analysis possibleRare in practice in water systems.

Transitional flow

2000 > Re < 4000

'medium' velocity

Dye stream wavers in water - mixes slightly.

Turbulent flowRe > 4000

'high' velocity

Dye mixes rapidly and completely

Particle paths completely irregular

Average motion is in the direction of the flow

Cannot be seen by the naked eyeChanges/fluctuations are very difficult to detect. Must use laser.

Mathematical analysis very difficult - so experimental measures are used

Most common type of flow.


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For cross sections other than circular, an equivalent diameter ,de,

defined as four times the hydraulic radius Rhis used instead of d.

de= 4 Rh= 4( area of flow /wetted perimeter)

E.g. 1

E.g. 2

deof annulus of inside dia diand

outside dia do=

dePipe of circular cross-section of

dia d=


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The units for parameters in the Reynolds number should

be consistent, so that a dimensionless number is

obtained.

d - ft

v - ft/sec

- lb m/ft3

- lb m /secFor all practical purposes the Reynolds number for

natural gas flow problems may be expressed as

NRe=20q g/ d

q = MMscfd

= cp

g = gas gravity

d = inches


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PIPEROUGHNESS

Absolute roughness: the absoluteroughness e of a pipe wall is defined as themean protruding height of relativelyuniformly distributed and sized, tightlypacked sand grains that would give thesame pressure gradient behavior as theactual pipe wall.

Relative roughness: it is the ratio of theabsolute roughness to the diameter of thepipe.

Relative roughness= /d15


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LAMINARSINGLEPHASEFLOW

The pressure drop for laminar flow is given by HagenPoiseuille relationship as follows:

p=32vl/gcd2

fv2 l /2gcd = 32 v l /gcd2

f= 32 *2/d v

= 64 /d v

f =64/NRe

Thus the friction factor is independent of pipe roughness

in the laminar flow regime.

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PARTIALLYTURBULENT& FULLYTURBULENT

SINGLEPHASEFLOW

For partially turbulent flow, friction factor is a

function of both Reynolds number and pipe

roughness. For fully turbulent flow , however the

friction factor is only very slightly dependentupon Reynolds number.

Several correlations have been reported for the

dependence of friction factors on Reynolds

number and pipe wall roughness.

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For smooth pipes:

f=0.5676NRe-0.3192for intermediate flow

f=16 log (NRef0.5/0.7063) for partially turbulentflow

f-0.5=2 log (NRef0.5/0.628) for fully turbulent flow

f=0.3614NRe

-0.25for NRe

up to 105

For rough pipes:

f-0.5=-2log [/(3.7d)+0.628/(NRef0.5)]

For very rough pipes:

f-0.5=-2log /(3.7d)

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ALLOWABLEWORKINGPRESSUREFORPIPES

To achieve higher throughputs a pipe can operate at high

pressure.

It is limited by the maximum stress the pipe can handle.

The maximum allowable internal working pressure can

be determined using ANSI specification:

p max=2(t-c)SE/do-2(t-c)Y

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Where

pmax=maximum allowable internal pressure, psig

t= pipe thicknessc=sum of mechanical allowances (thread and groove

depth), corrosion , erosion etc.,in.

S= allowable stress for the pipe material, psi

E=longitudinal weld joint factordo= outside diameter of the pipe, in.

Y= temperature derating factor

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ALLOWABLEFLOWVELOCITYINPIPES

High flow velocities in pipes can cause pipe erosion

problems, especially for gases that may have a flow

velocity exceeding 70 ft/sec.

The velocity at which erosion begins to occur is

dependent upon the presence of solid particles ,

their shape etc.

ve=C/0.5

In most cases C is taken to be 100.

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If c and are substituted then ve= -------------.

ve= 100(ZRT)0.5/(28.97pg)

0.5

The gas flow rate at standard conditions for erosion tooccur ,(qe)sc,can be obtained as follows:

(qe)sc= 1,012.435 d2(p/gZT)

0.5

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Unit-4 Gas Flow Fundamentals