AGA – Turbulent

Introduction

The Pipe Flow application calculates the values associated with the flow of gas through a pipe segment, including flow rate, inlet or outlet pressure, pressure drop, hydraulic diameter, minimum and maximum velocity, average pressure, line volume, and flowing compressibility. The American Gas Association – Turbulent (AGA – Turbulent) equation is one of several flow equations the application supports; this article covers the use of the Pipe Flow application with the AGA – Turbulent equation selected.

No single flow equation accurately reflects every condition that can occur in a gas piping system. The user is responsible for comparing the specific application against each equation’s intended use and selecting an appropriate equation. The AGA – Turbulent equation is intended for transmission systems operating under fully turbulent flow conditions.

Background

Various equations are available for calculating the volumetric flow through a pipe segment. Many were developed for a particular application or set of conditions, but nearly all are derived from a single general pipe flow equation. In general, every form states that the flow in a pipe segment is proportional to the pressure drop across the segment, divided by a combination of the pipe and gas resistance to flow. The larger the pressure drop, the higher the flow rate; the higher the resistance, the lower the flow rate.

Beyond this general relationship, each equation has been modified to reflect a certain flow regime or application-specific set of conditions. Separate equations have been developed to predict laminar or partially turbulent flow in low-pressure distribution systems, and to predict partially or fully turbulent flow in high-pressure, large-diameter, long-length transmission lines. The AGA family of equations falls into the transmission group.

Equation Selection Guidance

The reference documentation provides general application recommendations – offered for use at the User’s own risk – for matching a flow equation to an application. The following table summarizes those recommendations so the AGA – Turbulent equation can be placed in context against the alternatives.

Note: The AGA – Turbulent equation is a transmission-style equation for fully turbulent flow. It is moderately conservative relative to other transmission equations and is most appropriate where a fixed relative roughness and the rough pipe law are acceptable.

Pipe Roughness

As implemented in the calculator, the American Gas Association – Turbulent flow equation represents an equation with a fixed roughness parameter. It is applicable to transmission systems with fully turbulent flow conditions and uses a fixed relative pipe roughness with the rough pipe law. The method is moderately conservative compared with other transmission-style equations. It is distinct from the AGA – Fully Turbulent equation, which applies the rough pipe law with a variable roughness parameter, and from the AGA – Partially Turbulent equation, which applies the smooth pipe law.

Because the AGA – Turbulent equation uses a fixed roughness value, the Roughness data item is not used when this equation is selected. In practice, most pipe in natural gas service has a very smooth wall, either from well-manufactured steel or extruded plastic, and the wall condition tends to remain constant over time. Calibration studies of common flow equations indicate that, for the pipe materials and sizes commonly used in the gas industry, excluding an explicit wall-roughness term does not adversely affect results.

Pipe Efficiency

Most pipe flow equation will include a pipe efficiency term that allows the user to tune the equation so its results better match field-determined values. In most cases an efficiency of less than one is used to provide a margin of safety. As a general guideline, if an efficiency value below 0.80 or above 1.20 is required to match field results, there is either a problem with the entered data or the equation is a poor fit for the application.

Compressibility

The general flow relationship includes a compressibility term. Excluding compressibility, or assuming it to be unity (1.0), generally produces conservative results – that is, lower flow rates, higher pressure drops, or larger pipe sizes than would be obtained if compressibility were considered. The compressibility factor used during the calculation is governed by the Compressibility Factor Method set on the Base Conditions screen.

Equations

AGA – Turbulent Flow Equation

The AGA – Turbulent flow equation is expressed as follows:

Q = 1902.73 \times \dfrac{T_B}{P_B} \times \sqrt{\dfrac{\Delta P}{SG \times T_F \times L \times Z}}\times D^{2.584} \times E

Q = 1902.73 \times \dfrac{T_B}{P_B} \times \left( \dfrac{\Delta P}{SG \times T_F \times L \times Z} \right)^{0.5} \times D^{2.584} \times E

Where:
Q − Volumetric Flow Rate at the specified base pressure and temperature (ft³/hr)
T_B − Base Temperature (°R)
P_B − Base Pressure (psia)
ΔP − Pressure Drop term across the pipe segment, equal to P₁² − P₂² (psia²)
SG − Specific Gravity
T_F − Average Gas Flowing Temperature (°R)
L − Pipe Length (ft)
Z − Compressibility Factor
D − Inside Pipe Diameter (in)
E − Pipe Efficiency
P₁ − Pipe Inlet (Upstream) Pressure (psia)
P₂ − Pipe Outlet (Downstream) Pressure (psia)

Adjustment for Elevation

Where an elevation difference exists between the inlet and outlet of a pipe segment, the pressure-difference term in the flow equation is replaced to account for the hydrostatic head created by the weight of the gas. The replacement applies wherever the normal pressure difference is a function of the difference between the squared inlet pressure and the squared outlet pressure.

\Delta P = P_1^2 - e^{S} \times P_2^2

\Delta P = P_1^2 – e^{S} \times P_2^2

Where:
ΔP − Elevation-adjusted Pressure Drop term (psia²)
P₁ − Pipe Inlet (Upstream) Pressure (psia)
P₂ − Pipe Outlet (Downstream) Pressure (psia)
e − Napier’s Constant, 2.71828
S − Elevation Compensation Factor, computed as shown below

S = \dfrac{0.0375 \, SG \, (E_1 - E_2)}{T_F \times Z}

S = \dfrac{0.0375 \, SG \, (E_1 – E_2)}{T_F \times Z}

Where:
S − Elevation Compensation Factor
SG − Specific Gravity
E₁ − Pipe Inlet (Upstream) Elevation (ft)
E₂ − Pipe Outlet (Downstream) Elevation (ft)
T_F − Average Gas Flowing Temperature (°R)
Z − Compressibility Factor

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

Note: Pressure values are entered and displayed in gauge units, and flow values represent “standard” volume adjusted to the base conditions. If the Limit Pipe Velocity To Sonic preference is enabled and the flow exceeds the segment’s sonic (choked) capacity at the specified conditions, the calculation is limited to the maximum choked flow value. The number of decimal places shown for any calculated item can be set under File > Preferences > Decimals.

References

• Industrial Press, Gas Engineers Handbook, 1965.
• American Gas Association, Gas Engineering and Operating Practices – System Design, GEOP Series Book D-1, 1990.
• Gas Processors Suppliers Association, Engineering Data Book, Eleventh Edition – FPS, 1998.

FAQ