AGA Report No. 3

8/12/2019 AGA Report No. 3

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AGA Report No. 3

ORIFICE METERING OF NATURALGAS AND OTHER RELATED

HYDROCARBON FLUIDS

Part 3 Natural Gas Application

American Gas Association and AmericanPetroleum Institute 1992, 2003


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Symbols and Units


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Practical Orifice Flow Equation


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Mass Flow


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EQUATIONS FOR MASS FLOW OF

NATURAL GAS

The equations for the mass flow of natural

gas, in pounds mass per hour

The mass flow developed from the density of

the flowing fluid is expressed as :


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Mass flow developed from the ideal gas

relative density (specific gravity) expressed as


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The mass flow equation developed from real

gas relative density (specific gravity)


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EQUATIONS FOR VOLUME FLOW OF

NATURAL GAS

The volume flow rate of natural gas, in cubic

feet per hour at base conditions

The volume flow rate at base conditions, Qb,

developed from the density of the fluid at

flowing conditions and base conditions


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The volume flow rate at base conditions,

developed from ideal gas relative density

(specific gravity)


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the volume flow rate at base conditions,

developed from real gas relative density

(specific gravity)


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Standard Conditions


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The volume flow rate at standard conditions,

developed from the density of the fluid at

flowing conditions and standard conditions


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The volume flow rate at standard conditions,

developed from ideal gas relative density

(specific gravity)


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the volume flow rate at standard conditions,

developed from real gas relative density

,(specific gravity


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VOLUME CONVERSION FROM

STANDARD TO BASE CONDITIONS

If base conditions are different from standard

conditions, the volume flow rate calculated at

standard conditions can be converted to the

volume flow rate at base conditions throughthe following relationship


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Additional Computation


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DIAMETER RATIO

The diameter ratio ()

the ratio of the orifice bore diameter (d)t o the internal

diameter of the meter tube (0)

used in determining (a) the orifice plate coefficient of discharge,

(b) the velocity of approach factor

(c) the expansion factor


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COEFFICIENT OF DISCHARGE FOR

FLANGE-TAPPED ORIFICE METER

The coefficient of discharge for a flange-tappedorifice meter has been determined from testdata.

It has been correlated as a function of diameterratio (), tube diameter, and pipe Reynoldsnumber

The equation for the concentric, square-edged

flange-tapped orifice meter coefficient ofdischarge developed by Reader-Harris andGallagher


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Reader-Harris/Gallagher equation


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VELOCITY OF APPROACH FACTOR

mathematical expression that relates the

velocity of the flowing fluid in the orifice

meter approach section (upstream meter

tube) to the fluid velocity in the orifice platebore


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REYNOLDS NUMBER

The pipe Reynolds number (ReD) is used as a

correlation parameter to represent the change

in the orifice plate coefficient of discharge

with reference to the meter tube diameter,the fluid flow rate, the fluid density, and the

fluid viscosity


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=0.0000069 pounds mass per-foot-second

Standard Condition Tb = 519.67R, Pb = 14.73

psi, Zbair=0.999590


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If the fluid being metered has a viscosity,

temperature, or real gas relative density

(specific gravity) quite different from those

shown above, the assumptions are notapplicable.


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EXPANSION FACTOR

When a gas flows through an orifice, the changein fluid velocity and static pressure isaccompanied by a change in the density, and afactor must be applied to the coefficient to adjustfor this change.

The factor is known as the expansion factor

The expansion factor (Y) is a function of diameter

ratio, the ratio of differential pressure to staticpressure at the designated tap, and the isentropicexponent (k).


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Compressible Fluid Isentropic

Exponent

The real compressible fluid isentropic exponent,kr is a function of the fluid and the pressure andtemperature.

For an ideal gas, the isentropic exponent, ki, is

equal to the ratio of the specific heats (cp/cv) ofthe gas at constant pressure (cp) and constantvolume (cv) and is independent of pressure.

A perfect gas is an ideal gas that has constant

specific heats. The perfect gas isentropic exponent, kr is equal to

ki evaluated at base conditions


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It has been found that for many applications, the

value of kr is nearly identical to the value of ki,

which is nearly identical to kp. From a practical

standpoint, the flow equation is not particularlysensitive to small variations in the isentropic

exponent.

The perfect gas isentropic exponent, kp, is oftenused in the flow equation. Accepted practice for

natural gas applications is to use kp = k = 1.3.

The application of the expansion factor is valid


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The application of the expansion factor is valid

as long as the following dimensionless

criterion for pressure ratio is followed:


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Expansion Factor Referenced to

Upstream Pressure

If the absolute static pressure is taken at theupstream differential pressure tap, the value

of the expansion factor, Y:


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Expansion Factor Referenced to

Downstream Pressure

If the absolute static pressure is taken at the

downstream differential tap


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Compressibility Ideal and Real Gas

The terms ideal gas and real gas are used to

dene calculation or interpretation methods.

An ideal gas is one that conforms to the

thermodynamic laws of Boyle and Charles


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All gases deviate from the ideal gas laws to

some extent. This deviation is known as

compressibility and is denoted by the symbol

Z.


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Volume Base


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Compressibility at Base Condition

The value of Z at base conditions ( z b ) is

required and is calculated from the

procedures in A.G.A. Transmission

Measurement Committee Report No. 8.


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Supercompressibility

In orifice measurement, z b and 2, appear as a

ratio to the 0.5 power.

This relationship is termed the

supercompressibility factor and may be

calculated from the following equation


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RELATIVE DENSITY

The relative density (specific gravity) is

defined as a dimensionless number that

expresses the ratio of the density of the

flowing fluid to the density of a reference gasat the same reference conditions of

temperature and pressure.


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Ideal Gas Relative Density

The ideal gas relative density (specific gravity),Gi, is defined as the ratio of the ideal densityof the gas to the ideal density of dry air at the

same reference conditions of pressure andtemperature.

Since the ideal densities are defined at thesame reference conditions of pressure and

temperature, the ratio reduces to a ratio ofmolar masses (molecular weights).


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the ideal gas relative density (specific gravity)

is set forth in the following equation:

R l G R l ti D it (R l S ifi


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Real Gas Relative Density (Real Specific

Gravity)

Real gas relative density (specific gravity), Gr, isdefined as the ratio of the real density of the gasto the real density of dry air at the samereference conditions of pressure and

temperature To correctly apply the real gas relative density

(specific gravity) to the flow calculation, thereference conditions for the determination of the

real gas relative density (specific gravity) must bethe same as the base conditions for the flowcalculation.


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At reference (base) conditions (Pb, Tb), real

gas relative density (specific gravity) is

expressed as


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DENSITY OF FLUID AT FLOWING


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DENSITY OF FLUID AT FLOWING

CONDITIONS

The flowing density is a key component ofcertain flow equations.

defined as the mass per unit volume at

flowing pressure and temperature and ismeasured at the selected static pressure taplocation

The value for flowing density can becalculated from equations of state or from therelative density (specific gravity) at theselected static pressure tap.


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The fluid density at flowing conditions can also bemeasured using commercial densitometers.

Most densitometers, because of their physicalinstallation requirements and design, cannot

accurately measure the density at the selectedpressure tap location.

the fluid density difference between the densitymeasured and that existing at the defined pressure

tap location must be checked to determine whetherchanges in pressure or temperature have an impacton the flow measurement uncertainty


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Density Based on Gas Composition

When the composition of a gas mixture is

known, the gas densities t,p and pb may be

calculated from the gas law equations

The molecular weight of the gas may be

determined from composition data, using

mole fractions of the components and their

respective molecular weights


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Density Based on Ideal Gas Relative


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Density Based on Ideal Gas Relative

Density (Specific Gravity)

The following equations are applicable when a

gas analysis is available:


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Density Based on Real Gas Relative


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Density Based on Real Gas Relative

Density

The relationship of real gas relative density

(specific gravity) to ideal gas relative density


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INSTRUMENT CALIBRATION

Calibration standards for differential pressure

and static pressure instruments are often

used in the field without local gravitational

force adjustment or correction of the valuesindicated by the calibrating standards.

The manometer readings are affected by local

gravitational effects, water temperatures, andthe use of other than distilled water.


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Pressure devices that employ weights are also

used to calibrate differential pressure

instruments without correction for the local

gravitational force. Deadweight testers are used to calibrate static

pressure measuring equipment without

correction for the local gravitational force.


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It is usually more convenient and accurate toincorporate these adjustments in the flowcomputation than for the person calibrating theinstrument to apply these small corrections

during the calibration process. Therefore, additional factors are added to the

flow equation for the purpose of including theappropriate calibration standard corrections in

the flow computation either by the flowcalculation procedure in the office or by themeter technician in the field

Six factors are provided that may be used


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individually or in combination, depending on

the calibration device and the calibration

procedure used:

Volume flow equation


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Water Manometer Gas Leg Correction


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Water Manometer Gas Leg Correction

Factor (Fam)

The factor Fam corrects for the gas leg over

water when a water manometer is used to

calibrate a differential pressure instrument:


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When atmospheric air is used as the medium

to pressure both the differential pressure

instrument and the water U-tube manometer

during calibration, the density of air atatmospheric pressure and 60F must be

calculated using the following equation:


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AGA Report No. 3

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