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PRESSURE DROP CALCULATION EQUATIONS FOR PIPING AND PIPELINE

Ajay S. Satpute Sr. Process Engineer M. Tech. (Chemical) I.I.T., Madras, INDIA Ramboll Oil & Gas, QATAR Introduction: This spreadsheet is the compilation of pressure drop calculation equations for piping and pipeline. The purpose of this exercise is to have most reliable equations for pressure drop calculations at one place. YELLOW boxes are for input parameters and BLUE boxes are the calculated values.

PIPE SIZING Single phase (Liquid)

Single phase (Water)

Darcy - Weichbach equation (Ref. Crane handbook, 1986)

From Wikipedia Hazen–Williams equation Where;

Laminar

Turbulent

Pressure drop in meter water column L

Pipe length in meter

Q C d

Volumetric flow rate in m3/s Roughness coefficient Pipe ID in meter

Haaland equation (approximation of Colebrook White equation) Where; L V d

Pressure drop in Pa Darcy friction factor Pipe length in meter Liquid velocity in m/s Pipe ID in meter Reynold's number Relative roughness

198,851 0.021 100 3.438 5.00E-02 137,520 9.00E-04

ρ µ

Liquid density in kg/m3 Liquid viscosity in Pa.s

800 6.05E-04

PIPELINE SIZING Single phase (Crude oil) Service pipeline company equation (Ref. IPS-E-PR-440, March 1996) (For DN ≤ 750)

(For DN > 750)

(Laminar, if Nrem ≤ 0.135)

Where;

Pressure drop in kPa / 100 m Liquid flow rate in m3/hr f

S

Kinematic viscosity, m2/s Friction factor Pipe ID in mm Modified Reynold's number Specific gravity of liquid

267.9 24.3 1.00E-05 0.0068 50 2.2 (NRem = NRe / 7742) 0.8

Note: Darcy-Weichbach equation can also be used for liquids in PIPELINE.

(Turbulent)

17 50 0.00589 100 5.00E-02

PIPE SIZING Single phase (Gas) (≤ 12")

Where;

Single phase (Gas) (> 10") Weymouth equation

Panhandle equation

API 14E, 5th edition

API 14E, 5th edition

Gas flow rate in mmscfd

1.074

D P1 P2

Pipe ID in inch Upstream pressure in psia

L' S Z T1

Pipe length in ft Specific gravity of gas at standard condition Compressibility factor

Where;

Downstream pressure in psia

90 150 1 0.9961

Gas inlet temperature in oR

Gas flow rate in mmscfd D P1 P2

2 100

S Z T1

550

E

Note: Weymouth equation can be used for piping and pipeline for ID ≤ 12".

173.932

Pipe ID in inch Upstream pressure in psia

12 100

Downstream pressure in psia

90

Pipe length in miles Specific gravity of gas at standard condition Compressibility factor

0.028575 1 0.9961

Gas inlet temperature in oR

550

Efficiency factor; 1 for brand new pipe 0.95 for good operating conditions 0.92 for average operating conditions 0.85 for unfavorable operating conditions

1

Note: Panhandle equation can be used for piping and pipeline for ID > 10".

PIPELINE SIZING Single phase (Gas) (≤ 12")

Where;

Single phase (Gas) (> 10") Weymouth equation

Panhandle equation

API 14E, 5th edition

API 14E, 5th edition

Gas flow rate in mmscfd

1.074

D P1 P2 L'

Pipe ID in inch Upstream pressure in psia

2 100

Downstream pressure in psia Pipe length in ft

90 150

S

Specific gravity of gas at standard condition

Z T1

Compressibility factor Gas inlet temperature in oR

Where;

Gas flow rate in mmscfd D P1 P2

Pipe ID in inch Upstream pressure in psia

1

S

Specific gravity of gas at standard condition

0.9961

Z T1

Compressibility factor

E

Efficiency factor; 1 for brand new pipe 0.95 for good operating conditions 0.92 for average operating conditions

550

Downstream pressure in psia Pipe length in miles

Gas inlet temperature in oR

0.85 for unfavorable operating conditions

Note: Weymouth equation can be used for piping and pipeline for ID ≤ 12".

Note: Panhandle equation can be used for piping and pipeline for ID > 10".

173.932 12 100 90 0.028575 1 0.9961 550 1

PIPE SIZING Single phase (Gas) (Near atmospheric operating pressure lines)

Single phase (Steam)

Spitzglass equation

Babcock equation

API 14E, 5th edition

(From internet) Where;

Where;

Two phase

Gas flow rate in mmscfd Pressure drop in inch of water column D

Pipe ID in inch

S L'

Specific gravity of gas at standard condition Pipe length in ft

D W L' ρ'

0.0777 10 2

Modified Darcy equation API 14E, 5th edition

Pressure drop in psi Pipe ID in inch

7.3 2

Steam mass flow rate in lb/hr Pipe length in ft

1500 150

Steam density in lb/ft3

0.146

Erosional velocity equation API 14E, 5th edition Where;

1 150

f W D C

Note: Spitzglass equation can be used for piping and pipeline for single phase gas at near atmospheric operating pressure.

Note: Babcock equation can be used for piping and pipeline for steam.

Pressure drop in psi/100 ft

0.365

Erosional velocity in ft/s Moody / Darcy friction factor Mass flow rate in lb/hr

137.0 0.02 15000

Pipe ID in inch

6

Average mixture density, lb/ft3 Empirical constant 100 for continuous service 125 for non-continuous service

1 100

Note: Modified Darcy equation can be used for piping and pipeline for two phase fluid.

PIPELINE SIZING Single phase (Gas) (Near atmospheric operating pressure lines)

Single phase (Steam)

Spitzglass equation

Two phase Babcock equation

Modified Darcy equation

th

th

API 14E, 5 edition

API 14E, 5 edition Where;

Where;

Gas flow rate in mmscfd Pressure drop in inch of water column D S

Pipe ID in inch Specific gravity of gas at standard condition

L'

Pipe length in ft

0.0777 10 2 1

D W L' ρ'

Pressure drop in psi Pipe ID in inch

7.3 2

Steam mass flow rate in lb/hr Pipe length in ft

1500 150

Steam density in lb/ft3

0.146

150

Erosional velocity equation API 14E, 5th edition Where;

Pressure drop in psi/100 ft Erosional velocity in ft/s f

Moody / Darcy friction factor

W D

Mass flow rate in lb/hr

C

Note: Spitzglass equation can be used for piping and pipeline for single phase gas at near atmospheric operating pressure.

Note: Babcock equation can be used for piping and pipeline for steam.

0.365 137.0 0.02 15000

Pipe ID in inch Average mixture density, lb/ft3 Empirical constant 100 for continuous service 125 for non-continuous service

6 1 100

Note: Modified Darcy equation can be used for piping and pipeline for two phase fluid.

View more...
Ajay S. Satpute Sr. Process Engineer M. Tech. (Chemical) I.I.T., Madras, INDIA Ramboll Oil & Gas, QATAR Introduction: This spreadsheet is the compilation of pressure drop calculation equations for piping and pipeline. The purpose of this exercise is to have most reliable equations for pressure drop calculations at one place. YELLOW boxes are for input parameters and BLUE boxes are the calculated values.

PIPE SIZING Single phase (Liquid)

Single phase (Water)

Darcy - Weichbach equation (Ref. Crane handbook, 1986)

From Wikipedia Hazen–Williams equation Where;

Laminar

Turbulent

Pressure drop in meter water column L

Pipe length in meter

Q C d

Volumetric flow rate in m3/s Roughness coefficient Pipe ID in meter

Haaland equation (approximation of Colebrook White equation) Where; L V d

Pressure drop in Pa Darcy friction factor Pipe length in meter Liquid velocity in m/s Pipe ID in meter Reynold's number Relative roughness

198,851 0.021 100 3.438 5.00E-02 137,520 9.00E-04

ρ µ

Liquid density in kg/m3 Liquid viscosity in Pa.s

800 6.05E-04

PIPELINE SIZING Single phase (Crude oil) Service pipeline company equation (Ref. IPS-E-PR-440, March 1996) (For DN ≤ 750)

(For DN > 750)

(Laminar, if Nrem ≤ 0.135)

Where;

Pressure drop in kPa / 100 m Liquid flow rate in m3/hr f

S

Kinematic viscosity, m2/s Friction factor Pipe ID in mm Modified Reynold's number Specific gravity of liquid

267.9 24.3 1.00E-05 0.0068 50 2.2 (NRem = NRe / 7742) 0.8

Note: Darcy-Weichbach equation can also be used for liquids in PIPELINE.

(Turbulent)

17 50 0.00589 100 5.00E-02

PIPE SIZING Single phase (Gas) (≤ 12")

Where;

Single phase (Gas) (> 10") Weymouth equation

Panhandle equation

API 14E, 5th edition

API 14E, 5th edition

Gas flow rate in mmscfd

1.074

D P1 P2

Pipe ID in inch Upstream pressure in psia

L' S Z T1

Pipe length in ft Specific gravity of gas at standard condition Compressibility factor

Where;

Downstream pressure in psia

90 150 1 0.9961

Gas inlet temperature in oR

Gas flow rate in mmscfd D P1 P2

2 100

S Z T1

550

E

Note: Weymouth equation can be used for piping and pipeline for ID ≤ 12".

173.932

Pipe ID in inch Upstream pressure in psia

12 100

Downstream pressure in psia

90

Pipe length in miles Specific gravity of gas at standard condition Compressibility factor

0.028575 1 0.9961

Gas inlet temperature in oR

550

Efficiency factor; 1 for brand new pipe 0.95 for good operating conditions 0.92 for average operating conditions 0.85 for unfavorable operating conditions

1

Note: Panhandle equation can be used for piping and pipeline for ID > 10".

PIPELINE SIZING Single phase (Gas) (≤ 12")

Where;

Single phase (Gas) (> 10") Weymouth equation

Panhandle equation

API 14E, 5th edition

API 14E, 5th edition

Gas flow rate in mmscfd

1.074

D P1 P2 L'

Pipe ID in inch Upstream pressure in psia

2 100

Downstream pressure in psia Pipe length in ft

90 150

S

Specific gravity of gas at standard condition

Z T1

Compressibility factor Gas inlet temperature in oR

Where;

Gas flow rate in mmscfd D P1 P2

Pipe ID in inch Upstream pressure in psia

1

S

Specific gravity of gas at standard condition

0.9961

Z T1

Compressibility factor

E

Efficiency factor; 1 for brand new pipe 0.95 for good operating conditions 0.92 for average operating conditions

550

Downstream pressure in psia Pipe length in miles

Gas inlet temperature in oR

0.85 for unfavorable operating conditions

Note: Weymouth equation can be used for piping and pipeline for ID ≤ 12".

Note: Panhandle equation can be used for piping and pipeline for ID > 10".

173.932 12 100 90 0.028575 1 0.9961 550 1

PIPE SIZING Single phase (Gas) (Near atmospheric operating pressure lines)

Single phase (Steam)

Spitzglass equation

Babcock equation

API 14E, 5th edition

(From internet) Where;

Where;

Two phase

Gas flow rate in mmscfd Pressure drop in inch of water column D

Pipe ID in inch

S L'

Specific gravity of gas at standard condition Pipe length in ft

D W L' ρ'

0.0777 10 2

Modified Darcy equation API 14E, 5th edition

Pressure drop in psi Pipe ID in inch

7.3 2

Steam mass flow rate in lb/hr Pipe length in ft

1500 150

Steam density in lb/ft3

0.146

Erosional velocity equation API 14E, 5th edition Where;

1 150

f W D C

Note: Spitzglass equation can be used for piping and pipeline for single phase gas at near atmospheric operating pressure.

Note: Babcock equation can be used for piping and pipeline for steam.

Pressure drop in psi/100 ft

0.365

Erosional velocity in ft/s Moody / Darcy friction factor Mass flow rate in lb/hr

137.0 0.02 15000

Pipe ID in inch

6

Average mixture density, lb/ft3 Empirical constant 100 for continuous service 125 for non-continuous service

1 100

Note: Modified Darcy equation can be used for piping and pipeline for two phase fluid.

PIPELINE SIZING Single phase (Gas) (Near atmospheric operating pressure lines)

Single phase (Steam)

Spitzglass equation

Two phase Babcock equation

Modified Darcy equation

th

th

API 14E, 5 edition

API 14E, 5 edition Where;

Where;

Gas flow rate in mmscfd Pressure drop in inch of water column D S

Pipe ID in inch Specific gravity of gas at standard condition

L'

Pipe length in ft

0.0777 10 2 1

D W L' ρ'

Pressure drop in psi Pipe ID in inch

7.3 2

Steam mass flow rate in lb/hr Pipe length in ft

1500 150

Steam density in lb/ft3

0.146

150

Erosional velocity equation API 14E, 5th edition Where;

Pressure drop in psi/100 ft Erosional velocity in ft/s f

Moody / Darcy friction factor

W D

Mass flow rate in lb/hr

C

Note: Spitzglass equation can be used for piping and pipeline for single phase gas at near atmospheric operating pressure.

Note: Babcock equation can be used for piping and pipeline for steam.

0.365 137.0 0.02 15000

Pipe ID in inch Average mixture density, lb/ft3 Empirical constant 100 for continuous service 125 for non-continuous service

6 1 100

Note: Modified Darcy equation can be used for piping and pipeline for two phase fluid.

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