GAS FLOW

EQUATIONS
Recall : Fluid
Mechanics
 Recall : Fluid Mechanics

Pressure of fluid (including gas) in motion decreases

along the pipeline.
 ∆  𝑃 ∝𝑄
Volume of   𝑃∝ 1
∆
∆  𝑃 ∝ 𝜖 gas 𝐷
5

Pipe Diameter
roughness of pipe

∆  𝑃 ∝ 𝑆 ∆  𝑃 ∝ 𝐿
Factors
Specific affecting Distance
gravity pressure
drop
 Friction in Pipes

• Friction loss is the loss of pressure or “head” that

occurs in pipe or duct flow due to the effect of the
fluid's viscosity near the surface of the pipe or duct.

• Friction loss, which is due to the shear stress

between the pipe surface and the fluid flowing
within, depends on the conditions of flow and the
physical properties of the system. These conditions
can be encapsulated into a dimensionless number
Re, known as the Reynolds number
Flow Regime

Re < 2100

Re > 4000
 Reynolds Number (Re)

• 

but

Unlike liquid, gas is compressible!!!

(density and velocity are changing due to
temperature and pressure)
 Reynolds Number of Gas

• Gas volume is normally measured at standard

conditions since it varies throughout the pipeline.

• Standard conditions
• Temperature, T = 15°C
• Pressure, P = 1.013 bar

• Reynolds Number need to be modified into standard

conditions by applying mass flow rate concept (mass
constant) based on continuity equation.
 Reynolds Number of Gas

• 
• 

We know that;
• 

We know that;
• 

Where Where
Qs Gas flowrate, Sm3/h Qs Gas flowrate, MMSCFD
D Pipe internal diameter, mm D Pipe internal diameter, inch
µ Gas dynamic viscosity, cp µ Gas dynamic viscosity, cp
S Gas specific gravity S Gas specific gravity
 Head Loss Due to Friction

Fluid kinetic energy

Area of wetted conduit

Cross sectional area of conduit

 Head Loss Due to Friction

• 

Where;
: Friction energy loss per unit mass of fluid
: Average fluid kinetic energy
: Area of wetted conduit
: Cross sectional area of conduit
 Head Loss Due to Friction

• 
 Head Loss Due to Friction

• 

We can write;

Where f is the Fanning friction factor

 Head Loss Due to Friction

• 

There is another friction factor known as

Darcy friction factor; where

Darcy-Weisbach
Equation
In this class, we will use Darcy friction factor
 Energy Associated with Fluid
in Motion
•  Pressure as Energy Density

Kinetic Energy

Potential Energy
 Bernoulli Equation

•  Conservation of energy principle:“Energy is neither created nor

destroyed”

For a close system

Divide by mg
This is known as Bernoulli Equation
 Bernoulli Equation With
Friction Head Loss
• 

2 2
𝑃 𝑣 𝑃 𝑣
( )( )1 1 2 2
+ +𝑧1 = + +𝑧2 +h𝐿
𝜌𝑔 2𝑔 𝜌𝑔 2𝑔
Transmission and
Distribution Lines
General Gas
Flow Equation
 Derivation of Gas flow
Equation

Assumed as uniform flow

Based on Euler or Bernoulli's equation

Energy changes in the pipe based on

• Losses due to friction

• Increase due to gas expansion when pressure is
reduced
• Increase due to increase in kinetic energy when
velocity is increased
• Losses or increases due to temperature changes
 Assumptions

• the flow process is Isothermal

• the pipeline is horizontal
• changes in kinetic energy of the gas are negligible
• no mechanical work is done by or on the gas
• the flow is steady-state
• the energy loss due to friction is given by the Darcy-
Weisbach equation
• friction factor is not based on pressure and length of
pipe
• constant compressibility factor along the pipeline
 Simplified General Gas Flow
Equation (SI)

• 

L = pipe length, m f = Friction factor

D = Pipe diameter, mm S = Gas gravity
T = Gas temperature, K Ts = Standard temperature, (288 K)
P = Absolute gas pressure, bara Ps = Standard pressure, (1.01325 bar)
Q = Gas flow rate, SCMH P1 = Absolute inlet pressure, bara
Z = Gas compressibility factor, P2 = Absolute outlet pressure, bara
 Simplified General Gas Flow
Equation (Imperial)

• 

L = pipe length, ft f = Friction factor

D = Pipe diameter, inch S = Gas gravity
T = Gas temperature, °R Ts = Standard temperature, (520 °R)
P = Absolute gas pressure, psia Ps = Standard pressure, (14.7 psia)
Q = Gas flow rate, SCFH P1 = Absolute inlet pressure, psia
Z = Gas compressibility factor, P2 = Absolute outlet pressure, psia
 Efficiency Factor (E)

• The actual flow of gas in pipe can be significantly

smaller than that predicted by the relevant flow
equation.
• Factors that contribute to the deviation are:
• Actual pipe roughness
• Pipe joints, welds, etc
• Valves
• Bends, tees and other fittings
• Presence of dust and debris
 Efficiency Factor (E)

• The
  deviation could be represented by a fixed percentage.
This leads to the idea of efficiency factor that correct to
actual conditions.

• Efficiency usually takes values between 0.8 and 1.0

• New pipe: 1.0; good operating conditions: 0.95; average
operating conditions: 0.85
• Mohitpour et al. (2000) suggest E values between 0.92 and 0.97
• Osiadacz (1987) recommends for old piping it can be as low as
0.7
 Simplified General Gas Flow
Equation (SI)

• 

L = pipe length, m f = Friction factor

D = Pipe diameter, mm S = Gas gravity
T = Gas temperature, K Ts = Standard temperature, (288 K)
P = Absolute gas pressure, bara Ps = Standard pressure, (1.01325 bar)
Q = Gas flow rate, SCMH P1 = Absolute inlet pressure, bara
Z = Gas compressibility factor, P2 = Absolute outlet pressure, bara
 Simplified General Gas Flow
Equation (Imperial)

• 

L = pipe length, ft f = Friction factor

D = Pipe diameter, inch S = Gas gravity
T = Gas temperature, °R Ts = Standard temperature, (520 °R)
P = Absolute gas pressure, psia Ps = Standard pressure, (14.7 psia)
Q = Gas flow rate, SCFH P1 = Absolute inlet pressure, psia
Z = Gas compressibility factor, P2 = Absolute outlet pressure, psia
 Simplified General Gas Flow
Equation (SI)
•  Pipe Diameter:

Length:

Inlet and outlet pressures:

 Simplified General Gas Flow
Equation (Imperial)
•  Pipe Diameter:

Length:

Inlet and outlet pressures:

 Transmission Factor

•  There are a lot of flow equation used in gas

industry nowadays and it has the same pattern with
the General Gas Flow Equation

• The difference only on the derivation of friction

factor or transmission factor
 Simplified Derivative
Equations
• There are several simplified derivative equations
can be used to calculate gas flow in pipelines.

• Most of the equations are effective, but the

accuracy and applicability of each equation falls
within certain ranges of flow and pipe diameter.
 IGT Distribution Equation

• 

L = Pipe length, ft S = Specific gravity

D = Pipe diameter, inch Tb = Base temperature, (520 °R)
Tf = Flow temperature, °R Pb = Base pressure, (14.7 psia)
Q = Gas flow rate, MCFH P1 = Absolute inlet pressure, psia
µ = Gas viscosity, lbm/ft.s P2 = Absolute outlet pressure, psia
 Mueller Equation

• 

L = Pipe length, ft S = Specific gravity

D = Pipe diameter, inch Tb = Base temperature, (520 °R)
Tf = Flow temperature, °R Pb = Base pressure, (14.7 psia)
Q = Gas flow rate, MCFH P1 = Absolute inlet pressure, psia
µ = Gas viscosity, lbm/ft.s P2 = Absolute outlet pressure, psia
 Fritzsche’s Equation

• 

L = Pipe length, ft S = Specific gravity

D = Pipe diameter, inch Tb = Base temperature, (520 °R)
Tf = Flow temperature, °R Pb = Base pressure, (14.7 psia)
Q = Gas flow rate, MCFH P1 = Absolute inlet pressure, psia
P2 = Absolute outlet pressure, psia
 Fully Turbulent Equation

• 

L = Pipe length, ft S = Specific gravity

D = Pipe diameter, inch Tb = Base temperature, (520 °R)
Tf = Flow temperature, °R Pb = Base pressure, (14.7 psia)
Q = Gas flow rate, MCFH P1 = Absolute inlet pressure, psia
Zavg = Average compressibility factor P2 = Absolute outlet pressure, psia
= Relative roughness, inch
 Panhandle A Equation

• 

L = Pipe length, ft S = Specific gravity

D = Pipe diameter, inch Tb = Base temperature, (520 °R)
Tf = Flow temperature, °R Pb = Base pressure, (14.7 psia)
Q = Gas flow rate, MCFH P1 = Absolute inlet pressure, psia
P2 = Absolute outlet pressure, psia
 Spitzglass (High Pressure)
Equation
• 

L = Pipe length, ft S = Specific gravity

D = Pipe diameter, inch P1 = Absolute inlet pressure, psia
Q = Gas flow rate, MCFH P2 = Absolute outlet pressure, psia
 Spitzglass (Low Pressure)
Equation
• 

L = Pipe length, ft S = Gas gravity

D = Pipe diameter, inch = Pressure drop, in wc
Q = Gas flow rate, MCFH
 Weymouth Equation

• 

L = Pipe length, ft S = Gas gravity

D = Pipe diameter, inch Tb = Base temperature, (520 °R)
Tf = Flow temperature, °R Pb = Base pressure, (14.7 psia)
Q = Gas flow rate, MCFH P1 = Absolute inlet pressure, psia
P2 = Absolute outlet pressure, psia
 Other Equations

• Spitzglass (Medium Pressure) Equation

• Renouard (Low Pressure) Equation
• Renouard (Medium Pressure) Equation
• AGA Partially Turbulent Equation
• AGA Fully Turbulent Equation
• Panhandle B Equation
• Modified Colebrook-White Equation
• Gersten et al. Equation
Type of Piping Predominant Equation Used Range Applicability
Type of Flow in
Clean
Commercial
Pipe
High Pressure Partially Panhandle A Relatively good, slightly optimistic approximation for
utility supply Turbulent Smooth pipe Flow at Reynolds number >100,000
mains
Fully turbulent Weymouth Good approximation to Fully Turbulent Flow law for clears
rough commercial pipe of 10 to 30 inch diameter
Fully turbulent Accurately represents fully turbulent flow behaviour
Medium and Partially Panhandle A Relatively good, slightly optimistic approximation for
high turbulent Smooth pipe Flow at Reynolds number >100,000
distribution
Weymouth Very conservative for pipe of less than 20 in diameter
Spitzglass Very conservative
Fritzche Very conservative
IGT Distribution Excellent approximation for Smooth pipe Flow at Reynolds
number = 10,000 to 3,000,000
Low-pressure Partially Spitzglass Good approximation for Smooth pipe Flow for pipe 12 in.
distribution turbulent diameter and smaller
IGT Distribution Excellent approximation for Smooth pipe Flow at Reynolds
number = 10,000 to 3,000,000
Services Partially Mueller Excellent approximation for Smooth pipe Flow at Reynolds
turbulent number = 2,000 to 100,000
 Exercise 1

Natural gas with relative density 0.589 flows in a 150

mm diameter pipeline over a length 426 m where
the friction factor is 0.00534. If the inlet pressure is
33.3 mbar gauge and the outlet pressure is 27 mbar
gauge, calculate the gas flowrate in scmh.
 Exercise 2

Gas with relative density 0.6 is fed into a 200 mm

diameter pipeline at a rate of 20 MSCMH and a
pressure of 30 bar absolute. If the pipe line is 30 km
long, the average gas compressibility factor 0.92, the
average gas flowing temperature 20oC and has a
friction factor 0.003 at the stated flowrate, calculate
the down stream pressure.
 Exercise 3

Consider 1000 m of steel pipeline with an internal

diameter 100 mm. If the pipe inlet pressure is 10 barg and
the outlet pressure is 8 barg and others data as shown
below. Calculate Q using Panhandle A and friction factor.

Type of gas : Natural Gas

Relative density : 0.589
Dynamic viscosity : 0.01055 centipoise
Gas flowing temperature : 15oC
Gas Compressibility factor : 1.0
EFFECT OF
ALTITUDE TO
GAS FLOW
EQUATIONS
 Effect of Altitude on Low
Pressure System
• As mention in previous section, the equation
assumes the flow is horizontal. Where there are
altitude changes the gauge pressure at one end of
the pipe must be corrected relative to the other
before the equation can be used.
• The correction is required as atmospheric pressure
Patm decreases as altitude increase. At sea level, the
atmospheric pressure Patm is about 1.013 bar.
 Elevation effect

•   consider a gas piping with:

Let’s
Pg2
Patm2
Patm1, Paatm2 : atmospheric pressure at point 1 and 2
Pg1 , Pg2 : Gauge pressure of gas at point 1 and 2
h : difference of height between point 1 and 2

Pg1 Patm
Absolute pressure at point 2;
 Elevation effect

Pg2
•  Patm2

where density of air is 1.2248 kg/m3 and 1/102 converts

from N/m2 to mbar and then:
Pg1 Patm1
 Elevation effect
SG = 0.6 SG = 2.0
pressure pressure
elevation elevation
(m) difference (m) difference
(mbar) (mbar)
10 0.48 10 -1.20
20 0.96 20 -2.40
30 1.44 30 -3.60
40 1.92 40 -4.81
50 2.40 50 -6.01 It shows that elevation only
60 2.88 60 -7.21 affect significantly the low
70 3.36 70 -8.41
80 3.84 80 -9.61 pressure pipeline system
90 4.33 90 -10.81
100 4.81 100 -12.02
110 5.29 110 -13.22
120 5.77 120 -14.42
130 6.25 130 -15.62
140 6.73 140 -16.82
150 7.21 150 -18.02
 Pipe with Elevation (SI unit)

• 

Where

L = pipe length, m f = Friction factor

D = Pipe diameter, mm S = Gas gravity
T = Gas temperature, K Ts = Standard temperature, (288 K)
P = Absolute gas pressure, bara Ps = Standard pressure, (1.01325 bar)
Q = Gas flow rate, SCMH P1 = Absolute inlet pressure, bara
Z = Gas compressibility factor, P2 = Absolute outlet pressure, bara
H = Elevation, m
 Pipe with Elevation (Imperial
unit)
• 

Where

L = pipe length, ft f = Friction factor

D = Pipe diameter, inch S = Gas gravity
T = Gas temperature, °R Ts = Standard temperature, (520 °R)
P = Absolute gas pressure, psia Ps = Standard pressure, (14.7 psia)
Q = Gas flow rate, SCFH P1 = Absolute inlet pressure, psia
Z = Gas compressibility factor, P2 = Absolute outlet pressure, psia
H = Elevation, ft
 Pipe with Several Elevation

• 

Where
 Exercise 600 m

310 m
290 m L L
L 3 5
2
L
1
L
270 m 4
200 m
above datum

90 m

A gas pipeline with an internal diameter of 580 mm

has the following elevation profile. If the gas has a
relative density of 0.6, calculate the flowrate when
the inlet pressure is 70 bar and the outlet pressure is
20 bar. f  0.04 Z  0.92
o
T  20 C
avg avg

L1  17.5 km L2  20.2 km L3  23.0 km

L4  39.3 km L5  50.0 km
 Maximum Gas Velocity

• The maximum recommended velocity is 20 m/s.

• This is to prevent erosion of the pipe wall by gas

borne and debris.

• Therefore any calculations involving the section of

pipe sizes should always include a check to ensure
the velocity is reasonable.
 Maximum Gas Velocity

• Since the volume flowrate from the low pressure

equation is the actual volume, the resulting velocity
is also actual velocity. But the volume flowrate
calculated by high pressure equation is at standard
conditions, the figure should be corrected to actual
flowrate in order to calculate the actual velocity.

• Since the maximum velocity occurs at the point

where the pressure is lowest i.e. down stream
pressure P2, then correction should be made using
this pressure.
 Maximum Gas Velocity

• Correction
  can be made by using expressions shown below;

Where P2,abs is in bar

Then,

Or
PIPE
CONFIGURATIONS
 Equivalent Length

• Most of the gas supply systems consist of networks of

pipes which have been developed in stages over the
years.

• These networks can only be analyzed effectively using

network analysis techniques.

• However in many cases, particularly when considering

extensions or reinforcements, it is convenient to reduced
the problem by considering some pipes as equivalent in
length or diameter to other pipes in the system.
 Equivalent Length

•The
  general gas flow equation can be rearranged to form:

If the pressure loss is remain the same for both pipes

delivering similar Q, then;

This approach is applied in:

• Pipes in series
• Dual pipes