Orifice Meters

Introduction

This application calculates the values associated with the flow of gas through an orifice meter. Given the meter and tube dimensions, the differential and static pressures, the flowing temperature, and the relevant gas properties, the calculator can solve for the volumetric flow rate, the orifice size, and the associated meter tube and orifice velocities. Any single red-labeled item may be designated the “unknown” to be solved for, with all remaining red items treated as known.

The selected Calculation Method governs which standard is applied and imposes specific measurement requirements. The American Gas Association Report No. 3 (1992 and 2013) methods assume the differential pressure is measured at a flange tap location and are not valid for other tap locations. The International Standard Organization 5167 method assumes the static pressure is measured at the upstream tap location and is not valid for downstream measurement. A base pressure and temperature must be set on the Base Conditions screen, and an appropriate Compressibility Factor Method should be selected for accurate results.

Background

There are various methods and devices used to measure the flow of gas at a specific location; these devices are generally referred to as “meters.” An orifice meter uses the known characteristics of gas flowing through an orifice to determine the gas flow rate. The “orifice” is a reduced-size (relative to the inside tube diameter), sharp-edged circular opening in a plate placed in the path of the flow, configured so that gas can pass through the opening only. When installed correctly, these devices can provide very precise, accurate measurements. Various standards define the conditions, configurations, and equations required to produce results of a specified accuracy.

Flow through an orifice opening produces a pressure differential across the orifice plate, with the downstream pressure lower than the upstream pressure. With all other parameters held constant, the differential across the plate increases as the flow through the opening increases. By knowing the pressure and temperature conditions at the meter, the dimensional data for the orifice and the tube containing it, and certain gas properties, the volumetric flow through the orifice can be calculated. The various orifice meter calculation methods used in the gas industry expand on this fundamental relationship to varying levels of complexity. When the design and calculation methods described in the applicable standards are followed, a specific level of accuracy can be expected.

Temperature-Adjusted Dimensions

The orifice bore and the meter tube bore are specified at a dimensional reference temperature, but both expand or contract at the flowing temperature. The calculator adjusts each diameter from its reference temperature to the flowing temperature using the coefficient of linear thermal expansion of the respective material. The reported Orifice Velocity is based on the flow through the temperature-adjusted orifice diameter at the specified static pressure, and the reported Meter Tube/Pipe Velocity is based on the flow through the temperature-adjusted tube diameter at the specified static pressure.

Calculation Methods

The calculator provides several methods for calculating the parameters associated with an orifice meter. Each method is unique and may have specific limitations; the user must determine the appropriate method for the application being analyzed. The full details of each method are too extensive to reproduce here — refer to the cited references for the complete calculation procedures and parameter definitions.

American Gas Association Report No. 3 – 1985

This method uses the equations described in American Gas Association Report No. 3, “Orifice Metering Of Natural Gas,” Second Edition, 1985 (Reference 1).

American Gas Association Report No. 3 – 1992

This method uses the equations described in American Gas Association Report No. 3, “Orifice Metering Of Natural Gas,” Third Edition, 1992 (Reference 2). The calculations assume the differential pressure is measured using a flange tap location, and the method is not valid if the differential pressure is measured at another location.

American Gas Association Report No. 3 – 2013

This method uses the equations described in American Gas Association Report No. 3, “Orifice Metering Of Natural Gas…,” Fourth Edition, 2013 (Reference 4). The calculations assume the differential pressure is measured using a flange tap location, and the method is not valid if the differential pressure is measured at another location.

International Standard Organization 5167

This method uses the equations described in International Standard ISO 5167-1, “Measurement of fluid flow by means of pressure differential devices,” First Edition, 1991-12-15 (Reference 3). The calculations assume the static pressure is measured at the upstream tap location, and the method is not valid if the static pressure is measured at another location.

The orifice meter methods supported by the calculator build upon the general orifice mass-flow relationship defined by the cited standards. In this relationship, the mass flow rate is proportional to the square root of the differential pressure across the plate:

Equations

The mass flow rate for an orifice meter is calculated using the equation below:

q_m = \frac{C_d}{\sqrt{1 - \beta^4}}\, \varepsilon\, \frac{\pi}{4}\, d^2 \sqrt{2\, \Delta P\, \rho}

q_m = \frac{C_d}{\sqrt{1 – \beta^4}}\, \varepsilon\, \frac{\pi}{4}\, d^2 \sqrt{2\, \Delta P\, \rho}

Where:
q_m − Mass Flow Rate through the orifice
C_d − Orifice Plate Discharge Coefficient
β − Diameter Ratio, equal to d / D
ε − Expansion (Expansibility) Factor
d − Temperature-adjusted Orifice Bore Diameter (in)
D − Temperature-adjusted Meter Tube Internal Diameter (in)
ΔP − Differential Pressure across the orifice plate (in. H₂O)
ρ − Gas Density at flowing (upstream) conditions (lbm/ft³)

Note: The form above is the general governing relationship. Each supported method (AGA Report No. 3 — 1985, 1992, and 2013; and ISO 5167) implements the complete standard equations, including the standard-specific definitions of the discharge coefficient and expansion factor, the thermal-expansion corrections to the orifice and tube diameters, and the conversion from mass flow to volumetric flow at base conditions. Refer to the cited references for the full formulation. Unless otherwise noted, all values are in consistent dimensional units.

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

Note: The red-colored labels indicate which items may be calculated; an underlined label identifies the item selected as the unknown. Only one red item may be selected to be calculated, and all remaining items must be known. The number of decimal places shown for any calculated item can be set under File > Preferences > Decimals.

References

• American Gas Association, Report No. 3, Orifice Metering Of Natural Gas, Second Edition, 1985.
• American Gas Association, Report No. 3, Orifice Metering Of Natural Gas, Third Edition, 1992.
• International Standard Organization, ISO 5167-1, Measurement of fluid flow by means of pressure differential devices, First Edition, 1991.
• American Gas Association, Report No. 3, Orifice Metering of Natural Gas and Other Hydrocarbon Fluids – Concentric, Square-edged Orifice Meters, Part 3: Natural Gas Applications, Fourth Edition, November 2013.

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