AGA Fully Turbulent Flow

The AGA Fully Turbulent Flow equation is one of the more widely used flow rate equations for large diameter pipes, estimating pressure drops and flow rates with a strong degree of accuracy provided that an accurate estimate of the pipe roughness is known with correctness.

Formulas

AGA Equation

The transmission value for the AGA equation is calculated using the Von Karman equation:

F=4log_{10}biggr(frac{3.7D}{k}biggr)

F=4log_{10}\biggr(\frac{3.7D}{k}\biggr)

Where:
𝐹 − Transmission Factor
𝑘 − Pipe Roughness
𝐷 − Internal Diameter (in)

Using this transmission factor, we can calculate the flow rate, upstream pressure, downstream pressure, and predicted inner diameter of the pipe: Q=

EC_Q\cdot \left( \frac{T_b}{P_b} \right)\cdot \sqrt {\frac{P_1^2-e^sP_2^2}{GT_fL_eZ}}\cdot D^{2.5}

Q=E\cdot F\cdot C_Q\cdot \left( \frac{T_b}{P_b} \right)\cdot \sqrt   {\frac{P_1^2-e^sP_2^2}{GT_fL_eZ}}\cdot D^{2.5}

𝑄 − Flow Rate at Base Conditions (ft³/day)
E – Pipeline efficiency
𝐶_𝑄 − 38.77
𝑇_𝑏 − Base Temperature (°R)
𝑃_𝑏 − Base Pressure (psia)
𝑇_𝑓 − Gas Flowing Temperature (°R)
𝐷 − Internal Diameter (in)
𝑘 − Pipe Roughness (in)
𝑃₁ − Upstream Pressure (psia)
𝑃₂ − Downstream Pressure (psia)
𝐺 − Gas Specific Gravity
𝑍 − Compressibility Factor
L_e − Elevation-Adjusted Pipe Segment Length, including Expansion (mi, see below for definition)

s=frac{C_Striangle HG}{T_fZ}

s=\frac{C_S G\Delta H }{T_fZ}

𝑠 − Elevation adjustment parameter
𝐶_𝑆 − 0.0375
G – Gas specific gravity
∆𝐻 − Change in Elevation (ft) [Downstream Elevation (ft) – Upstream Elevation(ft)]
𝑍 − Compressibility Factor
𝑇_𝑓 − Gas Flowing Temperature (°R)

L_e=frac{(e^s-1)}{s}

L_e=\frac{(e^s-1)}{s}\times L

𝐿_𝑒 − Elevation-Adjusted Pipe Segment Length including Expansion (mi)
𝑠 − Elevation adjustment parameter
L – Pipe Segment Length including Expansion (mi)

Average Gas Velocity

The predicted average gas velocity from this system is:

V= 0.002122 \frac{Q}{D^2} \left(\frac{T_b}{P_b}\times \frac{P_\text{avg}}{T_f} \right)

V= 0.002122 \frac{Q}{D^2} \left(\frac{T_b}{P_b}\times  \frac{P_\text{avg}}{T_f}  \right) 

𝑉 − Average gas velocity (ft/sec)
𝑄 − Flow rate at base conditions (ft^3/hr)
𝐷 − Internal Diameter (in)
𝑇_𝑏 − Base Temperature (°R)
𝑃_𝑏 − Base Pressure (psia)
𝑇_𝑓 − Gas Flowing Temperature (°R)
𝑃_𝑎𝑣𝑔 − Average Internal Gas Pressure (psia)

For Small Pressure Drop (P2 > 0.8 P1):
P_{avg}=frac{(P_1-P_2)}{2}

P_{avg}=\frac{P_1-P_2}{2}

For large pressure drop :P_{avg}=
frac{2}{3}biggr[ P_1+P_2-frac{P_1P_1}{P_1+P_2} biggr]

P_{avg}=\frac{2}{3}\biggr[  P_1+P_2-\frac{P_1P_1}{P_1+P_2}    \biggr]

Sonic and Erosional Velocity

The predicted average gas velocity is checked against the sonic velocity of the gas, and the velocity at which erosion is predicted to occur on the pipe. If the gas exceeds the erosional velocity, operating at these conditions will cause long-term damage to the pipe; if the velocity exceeds the sonic velocity, the flow becomes choked, and the results of the AGA fully turbulent flow calculator are no longer applicable.

The erosional velocity of the gas is given by:
V_\text{errosion} = C_\text{errosion} \sqrt{10.73\cdot \frac{Z T_f}{29GP_\text{avg}}}

V_\text{errosion} = C_\text{errosion} \sqrt{10.73\cdot \frac{Z T_f}{29GP_\text{avg}}}

where:
𝑉_errosion − Erosional gas velocity(ft/sec)
C_errosion − Erosional gas constant (usually 100)
Z − Gas compressibility factor
𝑇_𝑓 − Gas Flowing Temperature (°R)
G − Gas specific gravity
𝑃_𝑎𝑣𝑔 − Average Internal Gas Pressure (psia)

The sonic velocity of the gas is given by:
V_\text{errosion} = C_\text{errosion} \sqrt{10.73\cdot \frac{Z T_f}{29GP_\text{avg}}}

V_\text{sonic} = 41.42\sqrt{\gamma_h \frac{T_f}{G}}

where:
𝑉_sonic − Sonic gas velocity(ft/sec)
𝑇_𝑓 − Gas Flowing Temperature (°R)
G − Gas specific gravity
𝑃_𝑎𝑣𝑔 − Average Internal Gas Pressure (psia)
γ_h – Sonic velocity constant
\gamma_h = 1.0836 -0.000115T_f +\frac{ 5.62 – 0.002T_f }{28.974G}

\gamma_h = 1.0836 -0.000115T_f +\frac{ 5.62 - 0.002T_f }{28.974G} 

Case Guide

Part 1: Create Case

Input Parameters

• Internal Pipe Diameter(in)
• Length of Pipeline(mi)
• Upstream Elevation(ft)
• Downstream Elevation(ft)
• Pipe Roughness Value (in)
• Pipeline Efficiency Factor
• Gas Operating Temperature(°F)
• Base Temperature(°F)
• Base Pressure(psia)
• Upstream Pressure(psig)
• Downstream Pressure(psig)
• Flow rate (MCFD)
• Gas Specific Gravity
• Compressibility Factor
• Erosional Velocity Constant

Downstream Pressure

Flow Rate

Internal Pipe Diameter

Upstream Pressure

Part 2: Outputs/Reports

Results

• Downstream Pressure(psig)
• Flow Rate(MCFD)
• Internal Pipe Diameter(in)
• Upstream Pressure(psig)
• Transmission Factor
• Velocity(ft/sec.)
• Erosional Velocity(ft/sec.)
• Sonic Velocity(ft/sec.)

Downstream Pressure

Flow Rate

Internal Pipe Diameter

Upstream Pressure

References

• McAllister, E. W., “Pipeline Rules of Thumb” Gulf Professional Publishing, Seventh Edition
• Menon, Shahi E., “Gas Pipeline Hydraulics”, Systek Technologies, Inc.
• Carroll, Landon and Hudkins, Weston R., “Advanced Pipeline Design”
• American Gas Association (AGA), “Reference: Eq-17-18, Section 17, GPSA”, Engineering Data Book, Eleventh Edition

FAQ