Part 2 Steady-State Flow of Gas Through Pipes

Oil and Gas Pipeline Design, Maintenance and Repair Dr. Abdel-Alim Hashem Professor of Petroleum Engineering Mining, Petroleum & Metallurgical Eng. Dept. Faculty of Engineering – Cairo University [email protected] [email protected]

Part 2: Steady-State Flow of Gas through Pipes PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١

INTRODUCTION • Pipes provide an economic means of producing and transporting fluids in large volumes over great distances • The flow of gases through piping systems involves flow in horizontal, inclined, and vertical orientations, and through constrictions such as chokes for flow control PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٢

ENERGY OF FLOW OF A FLUID

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

٣

BERNOULLI'S EQUATION V A2 PB V B2 ZA + + +Hp = ZB + + + hf γ 2g γ 2g PA

• • • •

P V Z Hp

• hf

= the pressure = the velocity = the height = the equivalent head added to the fluid by a compressor at A = represents the total frictional pressure loss between points A and B.

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

٤

VELOCITY OF GAS IN A PIPELINE Q =VA

M 1 =q 1 ρ1 = M 2 = q 2 ρ2

V 1 ρ1 = V 1 ρ

q1 = V 1 A1

M 1 = q 1 ρ1 = q 2 ρ 2 = q b ρb P1

ρ1

⎛ρ ⎞ q1 = q b ⎜ b ⎟ ⎝ ρ1 ⎠ ρ1 =

=Z1RT1

Pb ρb = Zb RTb

P1 Z1RT1

⎛ Pb ⎞ ⎛ T1 ⎞ ⎛ Z1 ⎞ q1 = q b ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ Tb ⎠ ⎝ P1 ⎠ ⎝ Zb ⎠

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

٥

VELOCITY OF GAS IN A PIPELINE ⎛ Pb ⎞⎛ T1 ⎞ q1 = qb ⎜ ⎟⎜ ⎟ Z 1 since Zb = 1.0 ⎝ Tb ⎠ ⎝ P1 ⎠

qb Z1 ⎛ Pb ⎞ ⎛ T1 ⎞ 4x 144qb Z1 ⎛ Pb ⎞ ⎛ T1 ⎞ V1 = ⎜ ⎟⎜ ⎟ = ⎜ ⎟⎜ ⎟ A ⎝ Tb ⎠ ⎝ P1 ⎠ πd 2 ⎝ Tb ⎠ ⎝ P1 ⎠

qb ⎛ Pb ⎞⎛ Z1T1 ⎞ V 1 = 0.002122 2 ⎜ ⎟⎜ ⎟ (USCS ) d ⎝ Tb ⎠ ⎝ P1 ⎠

• • • • • • •

V1 qb d Pb Tb P1 T1

= upstream gas velocity, ft/s = gas flow rate, measured at standard conditions, ft3/day = pipe inside diameter, in. = base pressure, psia = base temperature, °R (460 + °F) = upstream pressure, psia = upstream gas temperature, °R(460 + °F) PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

(SCFD)

٦

VELOCITY OF GAS IN A PIPELINE • Gas velocity at section 2 is given by qb ⎛ Pb ⎞⎛ Z2 T2 ⎞ V 2 = 0.002122 2 ⎜ ⎟⎜ ⎟ d ⎝ Tb ⎠ ⎝ P2 ⎠

• Gas velocity at any point in a pipeline is given by V = 0.002122

V = 14.739

qb ⎛ Pb ⎞ ⎛ ZT ⎞ ⎟⎜ ⎟ (USCS ) 2 ⎜ d ⎝ Tb ⎠ ⎝ P ⎠

qb ⎛ Pb ⎞ ⎛ ZT ⎞ ⎟⎜ ⎟ (SI ) 2 ⎜ d ⎝ Tb ⎠ ⎝ P ⎠ PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٧

EROSIONAL VELOCITY V max =

100

ρ • Vmax = maximum or erosional velocity, ft/s • ρ = gas density at flowing temperature, lb/ft3 V max = 100 • • • • •

Z R T γg P

ZRT 29γ g P

= compressibility factor of gas, dimensionless = gas constant = 10.73 ft3 psia/lb-moleR = gas temperature, oR = gas gravity (air = 1.00) = gas pressure, psia PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٨

Example 1 • A gas pipeline, NPS 20 with 0.500 in. wall thickness, transports natural gas (specific gravity = 0.6) at a flow rate of 250 MMSCFD at an inlet temperature of 60°F. Assuming isothermal flow, calculate the velocity of gas at the inlet and outlet of the pipe if the inlet pressure is 1000 psig and the outlet pressure is 850 psig. The base pressure and base temperature are 14.7 psia and 60°F, respectively. Assume compressibility factor Z = 1.00. What is the erosional velocity for this pipeline based on the above data and a compressibility factor Z = 0.90? PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٩

Solution • For compressibility factor Z = 1.00, the velocity of gas at the inlet pressure of 1000 psig is ⎛ 250x 105 ⎞ ⎛ 14.7 ⎞⎛ 60+460 ⎞ V 1 = 0.002122 ⎜ ⎟⎜ ⎟⎜ ⎟ = 21.29 ft/s 2 ⎝ 19.0 ⎠ ⎝ 60+460 ⎠⎝ 1014.7 ⎠

• Gas velocity at the outlet is ⎛ 1014.7 ⎞ V 2 = 21.29 ⎜ ⎟ = 24.89 ft/s ⎝ 864.7 ⎠

• The erosional velocity is found for Z = 0.90, V max = 100

0.9x 1014.7 x 250 = 53.33 ft/s 29x 0.6x 1014.7

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

١٠

REYNOLD’S NUMBER OF FLOW

ρV d Re = µ • • • •

Re V d ρ

• µ

(USCS )

= Reynolds number, dimensionless = average velocity of gas in pipe, ft/s = inside diameter of pipe, ft = gas density, lb/ft3 = gas viscosity, lb/ft-s PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١١

REYNOLD’S NUMBER OF FLOW

ρV d Re = µ • • • • •

(USCS )

USCS or SI Re = Reynolds number, dimensionless V = average velocity of gas in pipe, ft/s or m/s d = inside diameter of pipe, ft or m ρ = gas density, lb/ft3 or kg/m3

• µ

= gas viscosity, lb/ft.s or kg/m.s PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١٢

REYNOLD’S NUMBER OF FLOW IN CUSTOMARY UNITS ⎛ Pb R e = 0.0004778 ⎜ ⎝ Tb • • • • • •

Pb Tb γg q d µ

⎞⎛ γ gq ⎞ ⎟⎜ ⎟ (USCS ) ⎠ ⎝ µd ⎠

= base pressure, psia = base temperature, °R (460 + °F) = specific gravity of gas (air = 1.0) = gas flow rate, standard ft3/day (SCFD) = pipe inside diameter, in. = gas viscosity, lb/ft.s PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١٣

REYNOLD’S NUMBER OF FLOW IN CUSTOMARY UNITS ⎛ Pb R e = 0.5134 ⎜ ⎝ Tb • • • • • •

Pb Tb γg q d µ

⎞⎛ γ gq ⎞ ⎟⎜ ⎟ (SI ) ⎠ ⎝ µd ⎠

= base pressure, kPa = base temperature, °K (273 + °C) = specific gravity of gas (air = 1.0) = gas flow rate, standard m3/day (SCFD) = pipe inside diameter, mm = gas viscosity, Poise PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١٤

Flow Regime

• Re ≤ 2000 • 2000 > Re ≤ 4000 • Re > 4000

Laminar flow, Critical flow Turbulent flow

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

١٥

Example • A natural gas pipeline, NPS 20 with 0.500 in. wall thickness, transports 100 MMSCFD. The specific gravity of gas is 0.6 and viscosity is 0.000008 lb/ft.s. Calculate the value of the Reynolds number of flow. Assume the base temperature and base pressure are 60°F and 14.7 psia, respectively. PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١٦

Solution • Pipe inside diameter = 20 - 2 x 0.5 = 19.0 in. • The base temperature = 60 + 460 = 520 °R • Using Equation we get 6 ⎛ 14.7 ⎞ ⎛ 0.6x 100x 10 ⎞ R e = 0.0004778 ⎜ ⎟ = 5,331, 726 ⎟⎜ ⎝ 520 ⎠ ⎝ 0.000008x 19 ⎠

• Since Re is greater than 4000, the flow is in the turbulent region.

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

١٧

FRICTION FACTOR fd ff = 4 • ff = Fanning friction factor • fd = Darcy friction factor • For laminar flow 64 f = Re PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

١٨

FRICTION FACTOR FOR TURBULENT FLOW

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

١٩

INTERNAL ROUGHNESS Type of pipe e, in Drawn tubing (brass, lead, glass) 0.00006 Aluminum pipe 0.0002 Plastic-lined or sand blasted 0.0002-0.0003 Commercial steel or wrought iron 0.0018 Asphalted cast iron 0.0048 Galvanized iron 0.006 Cast iron 0.0102 Cement-lined 0.012-0.12 Riveted steel 0.036-0.36 PVC, drawn tubing, glass 0.000059 Concrete 0.0118-0.118 Wrought iron 0.0018 Commonly used well tubing and line pipe: New pipe 0.0005-0.0007 12-months old 0.00150 24-months old 0.00175

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

e,mm 0.001524 0.000508 0.00508-0.00762 0.04572 0.1292 0.01524 0.25908 0.3048-3.048 0.9144-9.144 0.0015 0.3-3.0 0.045 0.0127-.01778 0.381 0.04445

٢٠

TRANSMISSION FACTOR • The transmission factor F is related to the friction factor f as follows 2 F= f

4 f = 2 F

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

٢١

Relative Roughness

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

٢٢

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

٢٣

GENERAL FLOW EQUATION (USCS) ⎛ Tb q sc = 77.54 ⎜ ⎝ Pb • • • • • • • • • • •

qsc f Pb Tb P1 P2 γg Tav L Zav d

(

)

⎞ ⎛ P1 − P d ⎟⎜ ⎠ ⎜⎝ γ g Z avT av fL 2

2 2

5

⎞ ⎟ ⎟ ⎠

0.5

(USCS )

= gas flow rate, measured at standard conditions, ft3/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.

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

٢٤

Steady flow in a gas pipeline

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

٢٥

GENERAL FLOW EQUATION (SI) q sc • • • • • • • • • • •

(

)

⎛ P1 2 − P22 d 5 ⎛ ⎞ T = 1.1494 x 10 − 3 ⎜ b ⎟ ⎜ ⎝ Pb ⎠ ⎜⎝ γ g Z av T av f L qsc f Pb Tb P1 P2 γg Tav L Zav d

⎞ ⎟ ⎟ ⎠

0.5

(S I )

= gas flow rate, measured at standard conditions, m3/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

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

٢٦

General flow equation in terms of the transmission factor F ⎛ Tb q sc = 38.77 F ⎜ ⎝ Pb

(

)

⎞ ⎛ P1 − P d ⎟⎜ ⎠ ⎜⎝ γ g Z avT av L 2

2 2

5

⎞ ⎟ ⎟ ⎠

0.5

(USCS )

2 F= f

• F

(

)

⎞ ⎛ P1 − P d ⎟⎜ ⎠ ⎜⎝ γ g Z av T av L = transmission factor

⎛ Tb q sc = 5.747 x 10 F ⎜ ⎝ Pb −4

2

2 2

5

⎞ ⎟ ⎟ ⎠

0.5

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

(SI )

٢٧

EFFECT OF PIPE ELEVATIONS (

)

0.5

⎞ ⎛ P1 − e P d ⎞ ⎟ (USCS ) ⎟⎜ ⎠ ⎜⎝ γ g Z avT av Le ⎟⎠ 0.5 s 2 2 5 ⎛ ⎞ ⎛ T b ⎞ ( P1 − e P2 ) d −4 ⎟ (SI ) q sc = 5.747 x 10 F ⎜ ⎟ ⎜ ⎝ Pb ⎠ ⎜⎝ γ g Z av T av Le ⎟⎠ s ⎛T q sc = 38.77 F ⎜ b ⎝ Pb

2

s

2 2

5

(e - 1) Le = L s

s = (0.0375)γ g ( ∆z)/(Zav Tav ) (USCS) s = (0.0684)γ g (∆z)/(Zav Tav ) (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

٢٨

Gas flow through different elevations

(e s1 − 1) e s1 (e s 2 − 1) e s1 +s 2 (e s 3 − 1) e∑ Le = L1 + L2 + L 3 + ....... + s1 s2 s3

s n −1

(e s n − 1) Ln sn

si ≠ 0

(es - 1) j= s

Le = j 1L1 + j 2 L 2e s1 + j 3 L 3e s 3 + ....... + j n L n e s n −1 PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

si ≠ 0 ٢٩

AVERAGE PRESSURE IN PIPE SEGMENT P1P2 ⎞ 2 ⎛ Pav = ⎜ P1 + P2 + ⎟ P1 + P2 ⎠ 3 ⎝

• Or 2 ⎛ P13 − P23 ⎞ Pav = ⎜ 2 ⎟ 3 ⎝ P1 − P22 ⎠

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

٣٠

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

⎡ ⎛ 2.51 1 = −2 log ⎢ e +⎜ 3.7d ⎜ R f f ⎢⎣ ⎝ e

(

• • • •

)

⎞⎤ ⎟⎟ ⎥ Turbulent flow ⎠ ⎥⎦

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

٣١

COLEBROOK-WHITE EQUATION ⎛ 2.51 1 = −2 log ⎜ ⎜R f f ⎝ e

(

1 = −2 log e 3.7d f

)

⎞ ⎟⎟ Turbulent flow in smooth pipe ⎠

turbulent flow in fully rough pipes

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

٣٢

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.

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

٣٣

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.

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

٣٤

MODIFIED COLEBROOK-WHITE EQUATION ⎡ ⎛ 2.825 1 e = −2 log ⎢ +⎜ ⎜R f d 3.7 f ⎢⎣ ⎝ e

(

)

⎞⎤ ⎟⎟ ⎥ turbulent flow ⎠ ⎥⎦

⎡ ⎛ 1.4125F e F = −2 log ⎢ +⎜ 3.7 d ⎢⎣ ⎝ Re

(

)

⎞⎤ ⎟⎥ ⎠ ⎥⎦

with transmission factor

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

٣٥

AMERICAN GAS ASSOCIATION (AGA) EQUATION ⎛ 3.7d ⎞ F = 4 log ⎜ ⎟ Von Karman, for rough pipe ⎝ e ⎠ ⎛ Re ⎞ F = 4D f log ⎜ ⎟ Von Karman, smooth pipe ⎝ 1.412Ft ⎠

• 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 Ft = 4 log ⎜ ⎝ Ft

⎞ ⎟ − 0.6 ⎠

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

٣٦

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 total length of pipe section

Material

Bend Index Extremely Low 5° to 10°

Average 60° to 80°

Extremely High 200° to 300°

Bare steel

0.975-0.973

0.960-0.956

0.930-0.900

Plastic lined

0.979-0.976

0.964-0.960

0.936-0.910

Pig burnished

0.982-0.980

0.968-0.965

0.944-0.920

Sand blasted

0.985-0.983

0.976-0.970

0.951-0.930

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

٣٧

WEYMOUTH EQUATION ⎛ Tb q sc = 38.77 E ⎜ ⎝ Pb • • • • • • • • • • •

qsc f Pb Tb P1 P2 γg Tav Le Zav d

(

)

⎞ ⎛ P1 − e P d ⎟⎜ ⎠ ⎜⎝ γ g Z avT av Le 2

s

2 2

16 / 3

⎞ ⎟ ⎟ ⎠

0.5

(USCS )

= gas flow rate, measured at standard conditions, ft3/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

٣٨

WEYMOUTH EQUATION ⎛ Tb q sc = 3.7435x 10 xE ⎜ ⎝ Pb −3

• • • • • • • • • • •

qsc f Pb Tb P1 P2 γg Tav Le Zav d

(

)

⎞ ⎛ P1 − e P d ⎟⎜ ⎠ ⎜⎝ γ g Z avT av Le 2

s

2 2

16 / 3

⎞ ⎟ ⎟ ⎠

0.5

(SI )

= gas flow rate, measured at standard conditions,m3/day = friction factor, dimensionless 1/ 6 F = 6.521 d (SI ) = base pressure, kPa = 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

٣٩

PANHANDLE A EQUATION 1.0788

⎛ Tb ⎞ q sc = 435.87 E ⎜ ⎟ ⎝ Pb ⎠

(

1.0788

⎛ Tb ⎞ −3 q sc = 4.5965x 10 E ⎜ ⎟ ⎝ Pb ⎠ • E

)

⎛ P1 − e P ⎜ 0.8539 ⎜ γ g xT av xLe xZ ⎝ s

2

(

2 2

⎞ ⎟ ⎟ ⎠

0.5394

d 2.6182

)

⎛ P1 − e P ⎜ 0.8539 ⎜ γ g xT av xLe xZ ⎝ 2

s

2 2

⎞ ⎟ ⎟ ⎠

(USCS )

0.5394

d 2.6182

(SI )

= pipeline efficiency, a decimal value less than 1.0

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

٤٠

PANHANDLE A EQUATION Transmission Factor

⎛ qγ g ⎞ F = 7.2111E ⎜ ⎟ ⎝ d ⎠ ⎛ qγ g ⎞ F = 11.85E ⎜ ⎟ ⎝ d ⎠

0.07305

(USCS )

0.07305

(SI )

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

٤١

PANHANDLE B EQUATION 1.02

⎛ Tb ⎞ q sc = 737 E ⎜ ⎟ ⎝ Pb ⎠

(

1.02

⎛ Tb ⎞ q sc = 1.002x 10 E ⎜ ⎟ ⎝ Pb ⎠ −2

• E

)

⎛ P1 − e P ⎜ 0.961 ⎜ γ g xT av xLe xZ ⎝ 2

2 2

s

(

⎞ ⎟ ⎟ ⎠

0.51

d 2.53

)

⎛ P1 − e P ⎜ 0.961 ⎜ γ g xT av xLe xZ ⎝ 2

s

2 2

⎞ ⎟ ⎟ ⎠

(USCS )

0.51

d 2.53

(SI )

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

٤٢

PANHANDLE A EQUATION Transmission Factor

⎛ qγ g ⎞ F = 16.7 E ⎜ ⎟ ⎝ d ⎠ ⎛ qγ g ⎞ F = 19.08E ⎜ ⎟ ⎝ d ⎠

0.01961

(USCS )

0.01961

(SI )

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

٤٣

INSTITUTE OF GAS TECHNOLOGY (IGT) EQUATION ⎛ Tb q sc = 136.9E ⎜ ⎝ Pb

• µ

2 2

)

0.555

d 2.667

(USCS )

= gas viscosity, lb/ft.s

⎛ Tb q sc = 1.2822x 10 E ⎜ ⎝ Pb −3

• µ

(

⎞ P1 − e P ⎞⎛ ⎟ ⎟ ⎜ 0.8 0.2 ⎠ ⎜⎝ γ g xT av xLe xZx µ ⎟⎠ s

2

(

)

P1 − e P ⎞⎛ ⎟ ⎜ 0.8 0.2 ⎜ xT xL xZx γ µ av e ⎠⎝ g 2

s

2 2

⎞ ⎟ ⎟ ⎠

0.555

d 2.667

(SI )

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

٤٤

SPITZGLASS EQUATION Low Pressure

(

)

0.5

s ⎛ ⎞ − P e P ⎛ ⎞ T 1 2 3 ⎟ d 2.5 q sc = 3.839x 10 E ⎜ b ⎟ ⎜ ⎝ Pb ⎠ ⎝⎜ γ g xT av xLe xZ av (1 + 3.6 / d + 0.03d ) ⎟⎠

(USCS )

• Pressure less than or equal 1.0 psi

(

)

0.5

s ⎛ ⎞ − P e P ⎛ ⎞ T 1 2 −2 ⎟ d 2.5 q sc = 5.69x 10 E ⎜ b ⎟ ⎜ ⎝ Pb ⎠ ⎜⎝ γ g xT av xLe xZ av (1 + 91.44 / d + 0.03d ) ⎟⎠

(SI )

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

٤٥

SPITZGLASS EQUATION High Pressure

(

)

0.5

⎞ P1 − e s P2 ⎛ Tb ⎞ ⎛ ⎟ d 2.5 q sc = 729.608E ⎜ ⎟ ⎜ ⎝ Pb ⎠ ⎝⎜ γ g xT av xLe xZ av (1 + 3.6 / d + 0.03d ) ⎟⎠

(USCS )

• Pressure more than 1.0 psi

(

)

0.5

s ⎛ ⎞ P e P2 − ⎛ ⎞ Tb 1 −2 ⎟ d 2.5 q sc = 1.0815x 10 E ⎜ ⎟ ⎜ ⎝ Pb ⎠ ⎜⎝ γ g xT av xLe xZ av (1 + 91.44 / d + 0.0012d ) ⎟⎠

(SI )

• Pressure more than 6.9 kPa

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

٤٦

MUELLER EQUATION ⎛ Tb q sc = 85.7368E ⎜ ⎝ Pb

(

)

⎞ P1 − e P ⎞⎛ ⎟ ⎟ ⎜ 0.7391 0.2609 ⎟ ⎠ ⎜⎝ γ g xT av xLe x µ ⎠ 2

s

2 2

0.575

d 2.725

(USCS )

• µ = gas viscosity, lb/ft.s

(

)

2 2 s ⎛ ⎞ − P e P ⎛ ⎞ T 1 2 ⎟ q sc = 3.0398x 10−2 xE ⎜ b ⎟ ⎜ 0.7391 0.2609 ⎟ ⎝ Pb ⎠ ⎜⎝ γ g xT av xLe x µ ⎠

0.575

d 2.725

(SI )

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

٤٧

FRITZSCHE EQUATION ⎛ Tb q sc = 410.1688E ⎜ ⎝ Pb

⎛ Tb q sc = 2.827 E ⎜ ⎝ Pb

(

)

⎞ ⎛ P1 − e P ⎟ ⎜ 0.8587 ⎠ ⎜⎝ γ g xT av xLe

(

s

2

2 2

)

⎞ ⎛ P1 − e P ⎟ ⎜ 0.8587 ⎠ ⎜⎝ γ g xT av xLe 2

s

2 2

⎞ ⎟ ⎟ ⎠

⎞ ⎟ ⎟ ⎠

0.538

d 2.69

(USCS )

0.538

d 2.69

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

(SI )

٤٨

EFFECT OF PIPE ROUGHNESS

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

٤٩

COMPARISON OF FLOW EQUATIONS

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

٥٠

COMPARISON OF FLOW EQUATIONS

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

٥١

Flow Characteristics of LowPressure Services ⎡ total pressure drop in service, in H O ⎤ 2 ⎥ ft / hr = ⎢ ' ⎢⎣ ⎥⎦ ( K p ) γ / γ ( L + Lef ) 3

• • • • •

Kp γ γ' L Lef

(

0.54

)

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

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

٥٢

Values of Kp Pipe size and type

Kp

3/4-in CTS copper

1.622 x 10-6

1-in ID plastic

0.279 x 10-6

1-in CTS copper

0.383 x 10-6

1¼-in CTS copper

0.124 x 10-6

1¼-in NS steel

0.080 x 10-6

1½-in NS steel

0.037 x 10-6

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

٥٣

Equivalent lengths of pipe fittings • • • • • • • • • •

Fitting 1-in or 1¼-in Curb cock for copper service 1¼-in curb cock for 1¼-in steel service 1½-in curb cock for 1½-in steel service 1½-in street elbow for 1¼-in steel service 1½-in street elbow for 1½--in steel service 1¼-in street tee for 1¼-in steel service 1½-in street tee on sleeve or 1¼-in hole in main 1¼ x 1 x 1¼-in street tee 1½ x 1¼ x 1½-in street tee Combined outlet fittings • ¾-in copper • 1-in copper or plastic • 1¼-in steel • 1½-in steel

Equivalent length, ft 3.5 13.5 12.0 7.5 7.5 10.5 15.0 23.0 19.0

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

2.0 6.0 8.0 22.0

٥٤

Equivalent lengths of pipe fittings

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

٥٥

Flowing Temperature in (Horizontal]) Pipelines T Lx

⎡T s + C 4 / C 2 − (C 1C 5 ) / (C 2 (C 2 + C 3 ) ) ⎤ C 1C 2 /C 3 C + C L C (C + C L ) 3 x ⎦ 5 x =⎣ − 4 + 5 1 C 2 /C 3 C2 C 2 (C 2 + C 3 ) (C 1 + C 2 L x )

C 1 = z v 1c p L + (1 − z v 1 ) c p C2 = k / m

C 3 = ( z v 2 − z v 1 ) (c pL − c pv ) / L C4 =

z −z k πd 0 P1 − P2 v −v ⎡⎣ z v 1c pL µdL + (1 − z v 1 ) c pv µdv ⎤⎦ + v 2 v 1 Q + 2 1 v 1 + gh / L − T1 L L L m

z v 2 − z v 1 )( P1 − P2 ) ( v 2 −v 1 ⎡ ⎤ µ µ C5 = c c + + pv dv ⎦ 2 ⎣ pL dL L

L

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

٥٦

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

zv P L v cp µd m Q k g h do Ts

= mole fraction of vapor (gas) in the gas-liquid flowstream = pressure, lbf/ft2 = pipeline length, ft = fluid velocity, ft/sec = fluid specific heat at constant pressure, Btu/lbm.ºF = Joule-Thomson coefficient, ft2.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/sec2 = elevation difference between the inlet and outlet, ft = outside pipe diameter, ft = temperature of the soil or surroundings, of

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

٥٧

SUMMARY OF PRESSURE DROP EQUATIONS Equation General Flow

ColebrookWhite

Modified ColebrookWhite AGA

Application Fundamental flow equation using friction or transmission factor; used with Colebrook-White friction factor or AGA transmission factor Friction factor calculated for pipe roughness and Reynolds number; most popular equation for general gas transmission pipelines Modified equation based on U.S. Bureau of Mines experiments; gives higher pressure drop compared to original Colebrook equation Transmission factor calculated for partially turbulent and fully turbulent flow considering roughness, bend index, and Reynolds number

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

٥٨

SUMMARY OF PRESSURE DROP EQUATIONS Equation Panhandle A Panhandle B Weymouth

IGT

Application Panhandle equations do not consider pipe roughness; instead. an efficiency factor is used; less conservative than Colebrook or AGA Does not consider pipe roughness; uses an efficiency factor used for high-pressure gas gathering systems; most conservative equation that gives highest pressure drop for given flow rate Does not consider pipe roughness; uses an efficiency factor used on gas distribution piping

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

٥٩

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

٦٠

PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES

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

٦١

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 (Q1 + Q2) flowing through section BD. • At D, a branch pipe, DE, delivers a volume of Q3 to a customer location, E. • The remaining volume (Q1 + 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

٦٢

SERIES PIPING

• Segment 1 - diameter d1 and length Le1 • Segment 2 - diameter d2 and length Le2 • Segment 3 - diameter d3 and length Le3

Le = Le 1 + Le 2 + Le 3 PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٦٣

SERIES PIPING CL ∆Psq = 5 d • ∆Psq = difference in the square of pressures (P12 - P22) for the pipe segment • C = constant • L = pipe length • d = pipe inside diameter

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

٦٤

SERIES PIPING CL1 CLe 2 = 5 5 d1 d2 ⎛ d1 ⎞ Le 3 = L3 ⎜ ⎟ ⎝ d3 ⎠

Le 2

⎛ d1 ⎞ = L2 ⎜ ⎟ ⎝ d2 ⎠

5

5

5

⎛ d1 ⎞ ⎛ d1 ⎞ Le = L1 + L 2 ⎜ ⎟ + L3 ⎜ ⎟ ⎝ d2 ⎠ ⎝ d3 ⎠

5

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

٦٥

PARALLEL PIPING

Q = Q1 + Q2 where Q = inlet flow at A Q1 = flow through pipe branch BCE Q2 = flow through pipe branch BDE PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٦٦

PARALLEL PIPING

(P

2 B

−P

2 E

)

K 1L1Q12 = d 15

0.5

Q1 ⎛ L 2 ⎞ ⎛ d 1 ⎞ =⎜ ⎟ ⎜ ⎟ Q 2 ⎝ L1 ⎠ ⎝ d 2 ⎠

(P

2 B

−P

2 E

)

K 2 L 2Q 22 = 5 d2

2.5

where • K1, K2 = 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 PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٦٧

PARALLEL PIPING

(

PB2 − PE2 2 1

)

K e LeQ = d e5 2 2

LeQ L1Q L 2Q = = 5 5 d1 d2 d e5

2

2

K 1L1Q12 K 2 L 2Q 22 K e LeQ 2 = = 5 5 d1 d2 d e5

⎡⎛ 1 + const ⎞ 1 d e = d 1 ⎢⎜ ⎟ ⎢⎣⎝ const 1 ⎠

2 1/ 5

⎤ ⎥ ⎥⎦

5

⎛ d 1 ⎞ ⎛ L1 ⎞ const 1 = ⎜ ⎟ ⎜ ⎟ ⎝ d 2 ⎠ ⎝ L2 ⎠

Q1 = Q const1/(1 + const1 )

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

٦٨

LOCATING PIPE LOOP

Different looping scenarios PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٦٩

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

٧٠

Summary • Several piping configurations, such as pipes in series, pipes in parallel, and gas pipelines with injections and deliveries • The concepts of equivalent length in series piping and equivalent diameter in pipe loops were explained and illustrated using example problems. • The hydraulic pressure gradient and the need for intermediate compressor stations to transport given volumes of gas without exceeding allowable pipeline pressures were also covered. • The importance of temperature variation in gas pipelines and how it is taken into account in calculating pipeline pressures were introduced with reference to commercial hydraulic simulation models.. PE 607: Oil & Gas Pipeline Design, Maintenance & Repair

٧١