# Flow Rate and Pressure Drop of Gas Through a Pipeline

Calculation of Flow rate of gas through a pipeline.

## Flow Rate and Pressure Drop of Natural Gas Through a Pipeline

There are several formulas to calculate the flow rate, and some considerations should be taken for the proper use of them:

1. They are empirical, meaning that many elements on them are constants or values that are valid within a certain set of units and should be changed when considering another set of units. In this article, we are using Imperial units; thus, these formulas are not valid when using another set like, for instance, SI.
2. The applicability of these formulas has been tested in different conditions. It has been found out that some of them present more accurate results with the measured values under a certain range of conditions than others. So, the user should be careful when choosing which one to apply.
3. No difference in elevations is considered between the inlet and outlet points. If such a difference exists, its effect on pressure change requires a modification of the formula (not shown here) or shall be considered by other means.
4. The pressure ranges are above 100 psi.
For these formulas, the compressibility factor can be calculated with:

$P_{avg}=\frac{2}{3}(P_1+P_2-\frac{P_1*P_2}{P_1+P_2})$

• P1:Inlet Pressure, [psia]
• P2:Outlet Pressure, [psia]

$T_{avg}=\frac{T_1+T_2}{2}$

• T1:Inlet Temperature, [°R]
• T2:Outlet Temperature, [°R]
$Z_{avg}=\frac{1}{1+\frac{(3.444)(10^5)P_{avg}(10^{(1.785)S)}}{T_{avg}}}$
• S: Gas Specific Gravity, [dimensionless]

We will use four equations as presented by the GPSA (Gas Processors Suppliers Association):
• Weymouth.
• Panhandle A.
• Panhandle B.
• AGA (American Gas Association).

### Weymouth equation

Weymouth equation shall be used considering the following:
• The accuracy of the result decreases as the flow turbulence increases. Thus, this equation is good to be applied while Reynolds Number (Re) less than 2000. In case of more turbulent flow (Re>2000), other equations (Panhandle A, Panhandle B, or AGA) shall be used.
The equation is:

$Q=(433.5)(\frac{T_b}{P_b})E(\frac{P_1^2-P_2^2}{SL_mT_{avg}Z_{avg}})^{0.5}d^{2.667}$
• Q : Gas flow rate, [CFD], [cubic feet per day], [ft3/day] at base conditions.
• Tb : Base Temperature, equal to 520 [°R].
• Pb : Base absolute Pressure, equal to 14.76 [psia].
• E : Pipeline efficiency factor, [dimensionless].
• Lm : Pipeline length, [miles].
• d : Internal diameter, [in].

### Panhandle A equation

Panhandle A equation should be used with these considerations:
• The results with this equation show that when used with an Efficiency factor E between 0.9 and 0.92 (0.9 < E < 0.92), it fits better with partially turbulent flow. As the turbulence increases, its accuracy decreases. Thus, it is more suitable for Re between 2000 and 3000.
The equation is:

$Q=(435.87)(\frac{T_b}{P_b})^{1.0788}E(\frac{P_1^2-P_2^2}{S^{0.853}L_mT_{avg}Z_{avg}})^{0.5392}d^{2.6182}$

### Panhandle B equation

Panhandle B equation should be used with these considerations:
• The results with this equation show when used with E between 0.88 and 0.94, it approximates better to fully turbulent flow. Thus, it is more suitable for Re between 3000 and 4000.
The equation is:

$Q=(737)(\frac{T_b}{P_b})^{1.02}E(\frac{P_1^2-P_2^2}{S^{0.961}L_mT_{avg}Z_{avg}})^{0.51}d^{2.53}$

### AGA equation

The AGA equation should be used with these considerations:
• It is suitable for fully turbulent flow (Re>4000).

$Q=(38.77)(\frac{T_b}{P_b})E(4log_{10}(\frac{(3.7)(\frac{d}{12})}{\epsilon}))(\frac{P_1^2-P_2^2}{SL_mT_{avg}Z_{avg}})^{0.5}d^{2.5}$

Where

ε: Absolute roughness, (ft).

Material Absolute roughness (ft)
Drawn brass 0.000005
Drawn copper 0.000005
Commercial steel 0.00015
Wrought iron 0.00015
Asphalted cast iron 0.0004
Galvanized iron 0.0005
Cast iron 0.00085

Because Re depends on the velocity of the fluid defined by its flow rate, it is not possible to know Re until it is already calculated, which means that after Q is calculated, Re should be verified. So, the accepted Q result should be the one with the formula whose Re falls into its range.
The definition of Reynolds number is:

$R_e=\frac{VD\rho}{\mu_e}$

and

$D=\frac{d}{12}$

and

$V=\frac{Q_s}{A}$

where

Qs : Flow rate, [ft3/sec]=Q/((24) (60) (60))
V : Velocity, [ft/sec]
D : Diameter, [in]=d/12
A : Cross section Area, [ft2]
$\rho$ : gas density, [lb/ft3]
$\mu_e$ : gas viscosity, [lb/(ft*sec)]

Then, doing the substitutions with the already known variables above:

$R_e=\frac{Q_s}{(\pi\frac{D^2}{4})}D(\frac{\rho}{\mu_e})$

then
$R_e=\frac{4}{\pi D}(\frac{Q}{(24)(60)(60)})(\frac{\rho}{\mu_e})$
and
$R_e=(\frac{Q}{(1800)\pi d})(\frac{\rho}{\mu_e})$

Anyway, it is important to notice that there are many empirical numbers involved and the results follow certain assumptions, and there is no such accuracy as with a theoretically derived equation. That's why in many practical uses, the Weymouth equation is taken because of its conservative character.

#### Gas Flow Rate through Pipeline, CFD

Average Pressure, psia

Average Temperature, °R

Compressibility factor Zavg, (dimensionless)

#### Reynolds Number parameters

Digits after the decimal point: 3

Flow Rate, CFD

Reynolds Number

Flow Rate, CFD

Reynolds Number

Flow Rate, CFD

Reynolds Number

#### AGA formula

Flow Rate, CFD

Reynolds Number

URL copied to clipboard
PLANETCALC, Flow Rate and Pressure Drop of Gas Through a Pipeline