ECUACIONESDEFLUJOGAS

FLUJO EST ES TACIONARIO DE GAS POR GASODUCTOS

INTRODUCCION • Tubos proporcionan un medio económico económico de

producción y transporte de fluidos en gran volúmenes a grandes distancias • El flujo de gases a través de los sistemas sistemas de tuberías implica fluir en orientaciones horizontal, inclinado, y verticales, y a través constricciones tales como reducciones de control de flujo.

ENERGIA DE FLUJO DE UN FLUIDO

EQUATION BERNOULLI'S

• • • • •

P presion V velocidad Z altura H p el head equivalente adiciona al fluido por el compresor A hf representa la perdida de friccion total entre los puntos A y B

VELOCIDAD DEL GAS EN GASODUCTOS

VELOCIDAD DEL GAS EN GASODUCTOS

•

V1

• •

q b d Pb

= Flujo de Gas medido en condiciones standar, ft3/day (SCFD) = diametro interno, in. = presion base, psia

•

Tb

= base temperature, °R (460 + °F)

•

P1

= presion aguas arriba, psia

•

= velocidad del gas , ft/s

VELOCIDAD DEL GAS EN GASODUCTOS Velocidad del gas en la seccion 2 esta dada por:

Velocidad del gas en cualquier punto de la tuberia:

VELOCIDAD DE EROSION •

•

V max =maxima velocida de erosion en ft/s ρ

ρ

= densidad gas a temperatura de r flujo, lb/ft3 V max =100

ZRT 29 G P

• •

Z R

= factor de compresibilitdad del gas, = constante del gas = 10.73 ft3 psia/lb-mole ºR

•

T

= temperatura del gas , ºR

•

G

= Gravedad del gas (air = 1.00)

•

P

= Presion del gas, psia

Ejemplo 1 • Un gasoducto, DE 20 y 0.500 in. espesor , transports gas natural con una gravedad especifica de 0.6 y una relacion de flujo de 250 MMSCFD, la temperatura de 60°F. Asumiendo flujo isotermico. Calcular: La velocidad del gas inicial y final si la Presion inicial es de 1000 psig y la presion de salidad es 850 psig. La temperatura y presion base son 60 ºF y 14.696 psig respectivamente. Asumir el factor de compresibilidad Z= 1. Cual e sla velocidad de erosion en base a los datos de arriba y con un factor de compresibilidad de Z= 0.90? •

•

•

Solucion • Para un factor de compresibilidad Z = 1.00, la velocidad del gas a una presion inicial de 1000 psig es:

velocidad del gas a una presion final de 850 psig es:

La velocidad de erosion se encuentra para Z= 0.90 es:

  = 100√ 29 (.∗4.73∗5)

 = 100√ (∗.6∗4.66) = 53.33 ft/s

NUMERO DE REYNOLD’S   =  • • • •

R e V d ρ

• µ

(USCS -

SI

)

= numero de Reynolds = velocidad promedio del gas en la tuberia, ft/s - m/s = diametro interno, ft - m = densidad del gas gas , lb/ft3 - Kg/m3 = viscosidad del gas, lb/ft-s - Kg/m-s

NUMERO DE REYNOLD’S -USCS

• • • • • •

P b T b γg q d µ

= presion base, psia = temperatura base, °R (460 + °F) = gravedad especifica del gas (air = 1.0) = relacion de flujo, standard ft3/day (SCFD) = diametro interno, in. = viscosidad del gas, lb/ft.s

NUMERO DE REYNOLD’S - SI

• • • • • •

P b T b γg q d µ

= Presion base, kPa = temperatura base, °K (273 + °C) = gravedad especifica del gas (air = 1.0) = flujo de gas, standard m3/day (SCFD) = diametro interno, mm = viscosidad del gas, Poise

Regimen de Flujo • Re ≤ 2000

Laminar flow,

• 2000 > Re ≤ 4000

Critical flow

• Re > 4000

Turbulent flow

Ejemplo • Un gasoducto de OD=20 con 0.500 in. espesor, transporta 100 MMSCFD. La gravedad especifica del gas es de 0.60 y la viscosidad es 0.000008 lb/ft.s. Calcular el numero Reynolds. Asumir la temperatura y presion base 60°F y 14.696 psi, respectivamente.

Solucion •

•

Caudal Diametro interno

• Temperature base •

Viscosidad

= 100 Mmscfd = 20 - 2 x 0.5 = 19.0 in. = 60 + 460 = 520 °R = 0.000008 lb/ft-s

• Usando la ecuacion:

• Desde 4000 numero de Reynold se encuentra en flujo turbulento

FRICTION FACTOR

= f d

f f

4

• f f = Fanning friction factor • f d = Darcy friction factor • For laminar flow f

=

64

Re

FACTOR FRICCION PARA FLUJO TURBULENTO

INTERNAL ROUGHNESS Type of pipe Drawn tubing (brass, lead, glass) Aluminum pipe Plastic-lined or sand blasted

e, in 0.00006 0.0002 0.0002-0.0003

Commercial steel or wrought iron Asphalted cast iron Galvanized iron Cast iron Cement-lined Riveted steel PVC, drawn tubing, glass Concrete Wrought iron Commonly used well tubing and line pipe: New pipe 12-months old 24-months old

e,mm 0.001524 0.000508 0.00508-0.00762

0.04572 0.0018 0.1292 0.0048 0.01524 0.006 0.25908 0.0102 0.3048-3.048 0.012-0.12 0.9144-9.144 0.036-0.36 0.0015 0.000059 0.3-3.0 0.0118-0.118 0.045 0.0018 0.0005-0.0007 0.0127-.01778 0.381 0.00150 0.04445 0.00175

PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

TRANSMISSION FACTOR • The transmission factor F is related to the friction factor f as follows F =

f

2 f

= 4

F 2


Relative Roughness

Relative roughness =

e d

• e = absolute or internal roughness of pipe, in. • d = pipe inside diameter, in. PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

FLOW EQUATIONS FOR HIGH PRESSURE SYSTEM • • • • • • • • • • •

General Flow equation Colebrook-White equation Modified Colebrook-White equation AGA equation Weymouth equation Panhandle A equation Panhandle B equation IGT equation Spitzglass equation Mueller equation Fritzsche equation PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

GENERAL FLOW EQUATION (USCS) T b ( P 1 2 P )d  q sc = 77.54  fL  P b  Z gT av av   2

• • • • • • • • • • •

qsc f P b T b P1 P2 γg Tav L Zav d

2

5

0.5

(USCS )

= gas flow rate, measured at standard conditions, ft 3/day (SCFD) = friction factor, dimensionless = base pressure, psia = base temperature, °R( 460 + °F) = upstream pressure, psia = downstream pressure, psia = gas gravity (air = 1.00) = average gas flowing temperature, °R (460 + °F) = pipe segment length, mi = gas compressibility factor at the flowing temperature, dimensionless = pipe inside diameter, in.


Steady flow in a gas pipeline


GENERAL FLOW EQUATION (SI) q sc

(

)

0.5

5 2 d T b2  P 21  P 3  = 1.1494 x 10  (SI )   P b   Z g T av av fL 

• qsc • f • P b • T b • P1 • P2 • γg • Tav • L • Zav • d

= gas flow rate, measured at standard conditions, m 3/day = friction factor, dimensionless = base pressure, kPa = base temperature, °K (273 + °C) = upstream pressure, kPa = downstream pressure, kPa = gas gravity (air = 1.00) = average gas flowing temperature, °K (273 + °C) = pipe segment length, km = gas compressibility factor at the flowing temperature, dimensionless = pipe inside diameter, mm


General flow equation in terms of the transmission factor F d T b ( P 1 2 P )  q sc = 38.77 F    P b  Z gT av av L  2

F =

5

2

0.5

(USCS )

2 f

d T b( P 1 2 P )  q sc = 5.747 x10 F    P b  Z gT av av  L 4

• F

2

2

5

0.5

= transmission factor


(SI )

EFFECT OF PIPE ELEVATIONS 2

s

2

5

0.5

2

(USCS )

Z T L 2

0.5

s

4

 g Z avT av Le s

Le =

s

L

s = (0.0375)g(z)/(ZavTav)

(USCS)

s = (0.0684)g(z)/(ZavTav)

(SI)

• • •

s ∆Z e

= elevation adjustment parameter, dimensionless = elevation difference = base of natural logarithms (e = 2.718...) PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

Gas flow through different elevations

Le =

j=

Le

L1 + s1

L

(e s1 1)

+

2

s2

s3  1) e s1(e s2 1) e sn1 (e e s s1+n s  2(e 1) L 3 +.......+ Ln si sn s3

(es - 1) s

= j1 L1 + j2 L2e s + j3 L3e s +.......+ jn Lne s  1

3


n 1

si

 0

 0

AVERAGE PRESSURE IN PIPE SEGMENT  P 1 P 2  P P +  + 1 2 P av =  P + 3  P 1 2  2

• Or 3

P av =



2




COLEBROOK-WHITE EQUATION • A relationship between the friction factor and the Reynolds number, pipe roughness, and inside diameter of pipe. • Generally 3 to 4 iterations are sufficient to converge on a reasonably good value of the friction factor

1

(



= 2 log e f  

)

2.51   +   Turbulent flow 3.7d R e f  

• f = friction factor, dimensionless • d = pipe inside diameter, in. • e = absolute pipe roughness, in. • R e = Reynolds number of flow, dimensionless PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

COLEBROOK-WHITE EQUATION   2.51 = 2 log    Turbulent flow in smooth pipe f  Re f 1

1 f

(

) turbulent flow in fully rough pipes

= 2 log e3.7d


Example • A natural gas pipeline, NPS 20 with 0.500 in. wall thickness, transports 200 MMSCFD. The specific gravity of gas is 0.6 and viscosity is 0.000008 lb/ft-s. Calculate the friction factor using the Colebrook equation. Assume absolute pipe roughness = 600 µ in.


Solution • • • •

Pipe inside diameter = 20 - 2 x 0.5 = 19.0 in. Absolute pipe roughness = 600 ~ in. = 0.0006 in. First, we calculate the Reynolds number Re = 0.0004778(14.7/(60+460))x(( 0.6 x 200 x 106) /(0.000008x 19)) = 10,663,452

• This equation will be solved by successive iteration. • Assume f = 0.01 initially; substituting above, we get a better approximation as f = 0.0101. Repeating the iteration, we get the final value as f = 0.0101. Therefore, the friction factor is 0.0101.


MODIFIED COLEBROOK-WHITE EQUATION 1 f

(  )

 e = 2 log 3.7d

  2.825   turbulent flow + R e  f

e 1.4125 F  F =  2 log  with transmission factor 3.7d +  Re    

(

)


AMERICAN GAS ASSOCIATION (AGA) EQUATION 3.7d   e   Re  1.412 F t  • Df known as the pipe drag factor depend on bend index,

Its value ranges from 0.90 to 0.99 • Ft = Von Karman smooth pipe transmission factor

 Re  F t = 4log 0.6  F t  PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

Bend Index •

Bend index is the sum of all the angles and bends in the pipe segment, divided by the total length of the pipe section under consideration

BI =

total degrees of all bends in pipe section

Material

total length of pipe section BendIndex ExtremelyLow 5°to10°

Average 60°to80°

ExtremelyHigh 200°to300°

Baresteel

0.975-0.973

0.960-0.956

0.930-0.900

Plasticlined

0.979-0.976

0.964-0.960

0.936-0.910

Pigburnished

0.982-0.980

0.968-0.965

0.944-0.920

Sandblasted

0.985-0.983

0.976-0.970

0.951-0.930


WEYMOUTH EQUATION

(

)

0.5

T b  P 1 e2 P d   q sc = 38.77 E    P b   g Z avT av Le   2

• • • • • • • • • • •

qsc f P b T b P1 P2 γg Tav Le Zav d

s

2

16/3

(USCS )

= gas flow rate, measured at standard conditions, ft 3/day (SCFD) = friction factor, dimensionless F =11.18d 1/6

(USCS )

= base pressure, psia = base temperature, °R(460 + °F) = upstream pressure, psia = downstream pressure, psia = gas gravity (air = 1.00) = average gas flowing temperature, °R (460 + °F) = equivalent pipe segment length, mi = gas compressibility factor at the flowing temperature, dimensionless = pipe inside diameter, in. PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

WEYMOUTH EQUATION

(

)

0.5

 T b P 1 2e P d   q sc = 3.7435 x10 xE    P b   g Z avT av Le   3

• • • • • • • • • • •

qsc f P b T b P1 P2 γg Tav Le Zav d

2

s

2

16/3

(SI )

= gas flow rate, measured at standard conditions,m3/day = friction factor, dimensionless F = 6.521d 1/6 = base pressure, kPa (SI ) = base temperature, °K(273 + °C) = upstream pressure, kPa = downstream pressure, kPa = gas gravity (air = 1.00) = average gas flowing temperature, °K (272 + °C) = equivalent pipe segment length, km = gas compressibility factor at the flowing temperature, dimensionless = pipe inside diameter, mm PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

PANHANDLE A EQUATION 1.0788

q sc

T b  = 435.87 E    P b 

 ( P 12 e s P 2 2 )   0.8539  g xT av xLe xZ   

0.5394

1.0788

T b  q sc = 4.5965 x10 E    P b  3

• E

d 2.6182

 ( P e P 2 )   0.8539    g xT av xLe xZ  2 1

s

2

(USCS )

0.5394

d 2.6182

= pipeline efficiency, a decimal value less than 1.0


(SI )

PANHANDLE A EQUATION Transmission Factor 0.07305

q g  F = 7.2111 E    d 

(USCS )

0.07305

q g   F =11.85 E   d 

(SI )


PANHANDLE B EQUATION 1.02

T b   q sc = 737 E   P b 

 ( P e P 2 )  d 2.53 (USCS )  0.961    g xT a vxLe xZ  2 1

1.02

T b   q sc =1.002 x10 E   P b  2

• E

s

2

0.51

 ( P e P 2 )  d 2.53 (SI )  0.961    g xT av xLe xZ  2 1

s

2

0.51

= pipeline efficiency, a decimal value less than 1.0 PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

PANHANDLE A EQUATION Transmission Factor 0.01961

q g  F =16.7 E    d 

(USCS )

0.01961

q g   F =19.08 E   d 

(SI )


INSTITUTE OF GAS TECHNOLOGY (IGT) EQUATION

( P 2 e P ) d 2.667  T b (USCS ) 0.2   0.8 q sc =136.9 E  g xT av xLe xZx     P b  2

• µ

s

0.555

2 1

= gas viscosity, lb/ft.s

(

)

0.555

P e P 3 T b  2  0.2 d 2.667  0.8 q sc =1.2822 x10 E   xT xL av exZx  g  P b    2

• µ

s

2 1

= gas viscosity, Poise PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

(SI )

SPITZGLASS EQUATION Low Pressure

( P e P )

1 2 T b  = 3.839 x103 E    g xT av xLe xZ av (1+3.6/d +0.03d )  P b 

0.5

 (USCS d 2.5 ) 

s

q sc

• Pressure less than or equal 1.0 psi

( P e P )

1 2 T b  q sc = 5.69 x102 E   xT av xLe xZ av (1+91.44/d +0.03d ) g  P b  s

• Pressure less than or equal 6.9 kPa PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

0.5

  ) d 2.5 (SI 

SPITZGLASS EQUATION High Pressure

( P e P )

1 2 T b  = 729.608 E    g xT av xLe xZ av (1+3.6/d +0.03d )  P b 

0.5

s

q sc



(USCS  d 2.5 )



• Pressure more than 1.0 psi

( P 1e P 2 ) T b   q sc =1.0815 x102 E  g xT av xLe xZ av (1+91.44/d +0.0012d )  P b  s

• Pressure more than 6.9 kPa


0.5

  (SI ) d 2.5 

MUELLER EQUATION

(

)

0.575

  P 1 e P T b 2 (USCS ) 0.2609 d 2.725  0.7391 q sc =85.7368 E    P b g xT av xLe x  2

s

2

• µ = gas viscosity, lb/ft.s

T  2 b

q sc

• µ

s

= 3.0398 x102 xE   0.7391 xT av xLe x  g  P b 

( P

= gas viscosity, cP PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

e P 22)  (SI ) 0.2609 d 2.725  1

0.575

FRITZSCHE EQUATION  )  ( P 1 2 e P T b  d 2.69 (USCS ) q sc = 410.1688 E   0.8587  P b  g xT xL av   e 2

s

2

0.538

 )  ( P 1 2 e P T b  d 2.69 (SI ) q sc = 2.827 E   0.8587  P b   g xT xL av  e 2

s

2

0.538


EFFECT OF PIPE ROUGHNESS


COMPARISON COMP ARISON OF FLOW EQUATIONS


COMPARISON COMP ARISON OF FLOW EQUATIONS


Flow Characteristics of LowPressure Services

ft /hr =  3

total pressure drop in service, in H O  

• • • • •

K p γ γ' L Lef

( K )( p

)'  /

( L + L ) ef

= pipe constant = sp gr of gas = sp gr 0.60 = length of service, ft = equivalent length of fittings given below


0.54 2



 

Values of K p Pipesizeandtype

K p

3/4-inCTScopper

-6

1-inIDplastic

-6

1-inCTScopper

-6

1¼-inCTScopper

-6

1¼-inNSsteel

-6

1.622x10 0.279x10 0.383x10 0.124x10 0.080x10

-6 PE 607: Oil & Gas Pipeline Design, Maintenance & Repair 1½-inNSsteel 0.037x10

Equivalent lengths of pipe fittings Fitting •1-inor1¼-inCurbcockforcopperservice •1¼-incurbcockfor1¼-insteelservice •1½-incurbcockfor1½-insteelservice •1½-instreetelbowfor1¼-insteelservice •1½-instreetelbowfor1½--insteelservice •1¼-instreetteefor1¼-insteelservice •1½-instreetteeonsleeveor1¼-inholeinmain •1¼x1x1¼-instreettee •1½x1¼x1½-instreettee •Combinedoutletfittings •¾-incopper •1-incopperorplastic •1¼-insteel •1½-insteel


Equivalentlength,ft 3.5 13.5 12.0 7.5 7.5 10.5 15.0 23.0 19.0 2.0 6.0 8.0 22.0

Equivalent lengths of pipe fittings


Flowing Temperature in (Horizontal]) Pipelines T L x

T s +C 4 /C 2 (C 1C 5)/(C 2(C 2 +C 3/)C )  C 1C C 4 +C 5 L x  C /C C ( 1 2 L x ) +C

=

2

(

( +

C 5 C 1 +C 3 L x

3

2

3

)

C 1 = z v1c p L + 1 z v1 c p C 2 = k /m

) (c

(

C 3 = z v 2  z v1 C 4 =

L

pL

c pv)/ L

 z v1c pL dL +(1 z

)(

P  P 2 1 C 5 = z v 2  z v1 L

(

)c 

v1

) c  2

pv

dv

v 2 + + Q

L

+c   +v 2 1v pv dv   pL dL L


2

1

P 1  P 2 v 1 + gh / L  L

T 1

m

)

Flowing Temperature in (Horizontal]) Pipelines • • • • • • • • • • • • •

zv P L v c p µd m Q k g h do Ts

= mole fraction of vapor (gas) in the gas-liquid flowstream = pressure, lbf/ft 2 = pipeline length, ft = fluid velocity, ft/sec = fluid specific heat at constant pressure, Btu/lbm.ºF = Joule-Thomson coefficient, ft 2.ºF/lbf = mass flow rate, lbm/sec = phase-transition heat, Btu/lbm = thermal conductivity, Btu/ft.sec.ºf = gravitational acceleration, equal to 32.17 ft/sec 2 = elevation difference between the inlet and outlet, ft = outside pipe diameter, ft = temperature of the soil or surroundings, of


SUMMARY OF PRESSURE DROP EQUATIONS Equation

Application

GeneralFlow

Fundamentalflowequationusingfrictionor transmissionfactor;usedwithColebrook-White frictionfactororAGAtransmissionfactor

ColebrookWhite

Frictionfactorcalculatedforpiperoughnessand Reynoldsnumber; mostpopularequationforgeneralgastransmission pipelines

Modified ColebrookWhite

ModifiedequationbasedonU.S.BureauofMines experiments;giveshigherpressuredropcomparedto originalColebrookequation

AGA

Transmissionfactorcalculatedforpartiallyturbulent andfullyturbulentflowconsideringroughness,bend index,andReynoldsnumber PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

SUMMARY OF PRESSURE DROP EQUATIONS Equation

Application

PanhandleA PanhandleB

Panhandleequationsdonotconsiderpiperoughness; instead.anefficiencyfactorisused;less conservativethanColebrookorAGA

Weymouth

Doesnotconsiderpiperoughness;usesanefficiency factorusedforhigh-pressuregasgatheringsystems; mostconservativeequationthatgiveshighest pressuredropforgivenflowrate

IGT

Doesnotconsiderpiperoughness;usesanefficiency factorusedongasdistributionpiping PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES • A pipeline in which gas enters at the beginning of the pipeline and the same volume exits at the end of the pipeline is a pipeline with no intermediate injection or deliveries • When portions of the inlet volume are delivered at various points along the pipeline and the remaining volume is delivered at the end of the pipeline, we call this system a pipeline with intermediate delivery points. PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES


PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES

• Pipe AB has a certain volume, Q1, flowing through it. • At point B, another pipeline, CB, brings in additional volumes resulting in a volume of (Q 1 + Q2) flowing through section BD. • At D, a branch pipe, DE, delivers a volume of Q 3 to a customer location, E. • The remaining volume (Q 1 + Q2 - Q3) flows from D to F through pipe segment DF to a customer location at F. PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

SERIES PIPING

• Segment 1 - diameter d1and length Le1 • Segment 2 - diameter d2 and length Le2 • Segment 3 - diameter d3 and length Le3

Le

= Le1 + Le2 + Le3 PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

SERIES PIPING CL  P sq = 5 d • ∆Psq = difference in the square of pressures (P 12 - P22) for the pipe segment • C = constant • L = pipe length • d = pipe inside diameter


SERIES PIPING 5

CL1 d 15

 d 1   Le2 = L2  d 2 

= CLe2 d

5 2

5

d 1   Le3 = L3 d 3 

5 1

d   d 1  Le = L1 + L2   + L3  d 2  d 3  5


PARALLEL PIPING

Q = Q1 + Q2 where Q = inlet flow at A = flow through pipe branch BCE Q1 = flow through pipe branch BDE Q2

PARALLEL PIPING

( P  P )= K d LQ 2 B

2 E

1

1 12

15

( P  P )= K d LQ 2 B

2 E

2.5

0.5  L   d 1  2 Q1 =    Q2  L1  d 2 

where • K 1, K 2 = a parameter that depends on gas properties, gas temperature, etc. • L1 , L2 = length of pipe branch BCE, BDE • d1,d2= inside diameter of pipe branch BCE, BDE • Q1 , Q2 = flow rate through pipe branch BCE, BDE

2

2 2 5 2

PARALLEL PIPING

(

)

K e LeQ P B  P = E 2 d e 5

2

2 L1Q1 5 1

d

=

L 2Q22 LeQ 2 = d

5 2

d e 5

2

LQ 5

d 1

5

2

=

K LQ 5

d 2

K 1 L1

=

1

2 5

d e

1+const 1 2  1/5  d e =d 1     const 1 

 d 1   L 1     Q1 = Q const1/(1 + const1) const 1 =  d 2   L2 

2

2

LOCATING PIPE LOOP

Different looping scenarios

Summary • • • • • • •

This part introduced the various methods of calculating the pressure drop in a pipeline transporting gas and gas mixtures. The more commonly used equations for pressure drop vs. flow rate and pipe size The effect of elevation changes and the concepts of the Reynolds number, friction factor, and transmission factor were introduced. The importance of the Moody diagram and how to calculate the friction factor for laminar and turbulent flow were explained. Comparison of the more commonly used pressure drop equations, such as AGA, Colebrook-White, Weymouth, and Panhandle equations. The use of a pipeline efficiency in comparing various equations The average velocity of gas flow and the limiting value of erosional velocity was discussed .

ECUACIONESDEFLUJOGAS

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