Gas Measurement

Lecture 9

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Differential Pressure Flowmeters

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 Volumetric Measurement
 Natural Gas is transported in pipelines with continuous flow from
the gas reservoir to its ultimate user.
 Accurate measurement of the total quantity of gas that
has passed through a given section of pipe over a period
of time in a paramount importance to both gas sellers and
purchasers.
 The commonly used method of measurement of natural
gas is by volume.
 Because natural gas is compressible (volume depends
on Pressure and Temperature), to measure gas flow in
meaningful terms by the volume method, first specifying
the base, or standard, pressure and temperature is a 4
fundamental importance.
 Most operators account for gas in units of 1000 𝐟𝐭 𝟑 at predefined
standard conditions (pressure and temperature), commonly
referred to as one 𝐌𝐬𝐜𝐟.
 The American Petroleum Institute (API) and the American Gas
Association (AGA) have been using 14.73 psia and 60℉ as their
standard.
 Orifice meters are the most common equipment used in natural
gas industry for measurement of natural gas flow rate.
 An orifice meter consists of a thin plate with an accurately
machined circular hole that is centered in a pair of flanges or
other plate-holding device in a straight section of smooth pipe.
 Pressure tap connections are provided on the up-stream and
downstream sides of the plate so that ∆𝑷 or differential pressure
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may be measured.
Orifice meter

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Orifice meter

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Orifice meter

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Orifice meter

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Pipe Taps Orifice Meter

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Orifice Meter in Process

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Advantages of orifice meter
1. Simple design: Easy to construct and install.
2. Low cost: Cheaper compared to many other flow measurement
devices.
3. No moving parts: Reduces maintenance needs and increases
durability.
4. Suitable for a wide range of fluids: Can measure gases, liquids,
and steam.
5. Good accuracy: Especially when installed correctly and
calibrated.
6. Compact size: Does not require much space in the pipeline.
7. Standardization: Widely accepted for gas measurement by the
joint of AGA-ASME committee 14
8. Availability of the standard tables of meter factors
 Components of Orifice Meter
A. The primary element consists of:
1. Meter tube,
2. Orifice plate
3. Pressure taps
4. Straightening vanes which is a
device that may be inserted in the
upstream section of the meter
tube to reduce swirling in the gas stream.
B. The secondary element is a gauge (or gauges) connected with
tubing to the up-stream and down-stream pressure taps of the
primary element.
 One part indicates or records the difference between the pressure
on each side of the orifice plate (𝒉𝒘 ) and the other part indicates or
records one of these pressures (𝑷𝒇 ). 15
Straightening vanes are devices placed upstream of an orifice plate to ensure that the
flow of fluid (gas or liquid) entering the orifice is as uniform and streamlined as possible.
Why they are important:
a. When fluid flows through a pipe, especially after elbows, bends, valves, or other disturbances, the flow
can become swirly or turbulent.
b. This distorted flow can cause incorrect pressure readings across the orifice plate, leading to measurement
errors.
c. Straightening vanes help to eliminate swirl and asymmetry, creating a more stable, straight flow profile
before the fluid reaches the orifice.

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 Orifice Equation
 The basis for the orifice-meter equation is the first law of thermodynamics for
open system.
 𝒒𝒉 = 𝑪′ 𝒉𝒘 𝑷𝒇
Where:
 𝒒𝒉 = quantity rate of flow at base conditions, 𝒔𝒄𝒇𝒉
 𝑪′ = Orifice flow constant
 𝒉𝒘 = Differential pressure in inches of water at 𝟔𝟎𝟎 𝑭
 𝑷𝒇 = Absolute static pressure, 𝒑𝒔𝒊𝒂

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 The orifice constant (C’) is expressed in the following equation
 C’=(𝑭𝒃 )(𝑭𝒓 )(𝒀)(𝑭𝑷𝒃 )(𝑭𝒕𝒃 )(𝑭𝒕𝒇 )(𝑭𝒈 )(𝑭𝑷𝑽 )(𝑭𝒎 )(𝑭𝒍 )(𝑭𝒂 )
 Where:
 𝑭𝒃 = Basic Orifice Factor, 𝒄𝒇𝒉.
 𝑭𝒓 = Reynolds number factor.
 𝒀 = Expansion factor
 𝑭𝒑𝒃 = Pressure base factor
 𝑭𝒕𝒃 = Temperature base factor
 𝑭𝒕𝒇 = Flowing temperature factor
 𝑭𝒈 = Specific gravity factor
 𝑭𝒑𝒗 = Super compressibility Factor
 𝑭𝒎 = Manometer Factor for mercury meter
 𝑭𝒍 = Gauge location factor
 𝑭𝒂 = Orifice thermal expansion factor 18
1. 𝐅𝐛 is basic orifice factor, this factor depends on:
a. Location of the taps (Flange or Pipes)
b. The internal diameter of the run
c. The size of the orifice (Orifice Diameter)
 Tables for 𝐅𝐛 are present in appendix C-1, pp304-309 – Flange Tap,& C-6, pp
322-327-Pipe taps

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2. 𝐅𝐫 is Reynold’s Number factor, this factor depends on:
a. Viscosity, density and velocity of the gas
b. The Pipe diameter
𝐛
• 𝐅𝐫 = 𝟏 +
𝐡𝐰 𝐏𝐟
 Values of 𝐛 are given in appendix C-2, pp311-315- Flange Taps, C-
6, pp328-333 – Pipe taps.

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3. 𝐘 is the expansion factor
 This factor depends on the expansion of the gas through the orifice.
 The expansion factor is a function of:
a. The differential pressure (𝒉𝒘 )
b. The absolute pressure (𝑷𝒇 )
c. The diameter of the pipe
d. The diameter of the orifice
e. Type of Taps
𝒅𝒐𝒓𝒊𝒇𝒊𝒄𝒆 𝒅𝟎
 𝜷= =
𝑫𝒑𝒊𝒑𝒆 𝑫𝒑
 Tables of Y values are present in appendix C-3, pp316-317, C-4, pp318-319, C-5, pp320-321.

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4. 𝐅𝐏𝐛 is the pressure base factor, it is a direct application of Boyle’s law in the
correction for the difference in the base from 𝟏𝟒. 𝟕𝟑 𝐩𝐬𝐢𝐚.
𝟏𝟒.𝟕𝟑
 𝑭𝑷𝒃 = 𝑷𝒃 =base pressure in 𝐩𝐬𝐢𝐚
𝑷𝒃
5. 𝐅𝐭𝐛 is the temperature base factor, it is a direct application of Charle’s law in the
correction for the base temperature 𝟔𝟎𝟎 𝐅
𝒕𝒃 +𝟒𝟔𝟎
 𝑭𝒕𝒃 = 𝒕𝒃 = base temperature in ℉
𝟓𝟐𝟎
6. 𝐅𝐭𝐟 is the flowing temperature factor, this factor corrects the effect of temperature
variations.
 The flowing temperature has two effects on volume:
a) A higher temperature means a lighter gas so that flow will increase.
b) A higher temperature causes the gas to expand, which reduces the flow.
 These two combined effects is to cause the quantity of flow of gas to vary inversely as
the square root of the absolute temperature.
 The 𝐅𝐭𝐟 is usually applied to the average temperature during the time gas is passing.
𝟓𝟐𝟎
 𝑭𝒕𝒇 = 𝒕𝒇 = fluid temperature, ℉ 23
𝒕𝒇 +𝟒𝟔𝟎
7. 𝐅𝐠 is the specific gravity factor, it is used to correct for changes in the specific
𝟏
gravity. 𝑭𝒈 =
𝜸𝒈
8. 𝐅𝐏𝐕 is the super compressibility factor, it is used to correct for the fact that gas does
not follow the ideal gas law.
 It varies with temperature, pressure and specific gravity.
 Where Z is the compressibility factor.
 This factor is important at high line pressures
 𝐙 should be measured at 𝐏𝐟 (Absolute static pressure, 𝐩𝐬𝐢𝐚 ) 𝐚𝐧𝐝 𝐭 𝐟 𝐢𝐧 𝟎 𝑹 ,
𝟏
𝑭𝑷𝑽 =
𝒛
9. 𝐅𝐦 is the manometer factor, it is used with mercury differential gauges and compensates
for the column of compressed gas opposite to the mercury leg.
 Usually, this is not considered for pressure below 500 𝐩𝐬𝐢𝐚, nor is it required for
mercury-less differential gauges.

𝒉𝒘
𝑷𝒂𝒕𝒎 + 𝟐𝟕.𝟕𝟎𝟕
𝟔𝟐.𝟑𝟔𝟔𝟑 −
• 𝑭𝒎 = 𝟏𝟗𝟐.𝟒 24
𝟔𝟐.𝟑𝟔𝟔𝟑
10. 𝐅𝐥 is the gauge location factor, it is used where orifice meters are installed at
locations other then 45° latitude and sea level elevation.

𝒈
 𝑭𝒍 =
𝟑𝟐.𝟏𝟕𝟒𝟎𝟓
 Where:
 𝑳 = Latitude
 𝑯 = Elevation above sea level, ft.

 𝒈 = 𝟑. 𝟐𝟖𝟎𝟖 ∗ 𝟏𝟎−𝟐 𝟗. 𝟕𝟖𝟎𝟏𝟖𝟓𝟓 ∗ 𝟏𝟎𝟐 − 𝟐. 𝟖𝟐𝟒𝟕 ∗ 𝟏𝟎−𝟑 𝑳 + 𝟐. 𝟎𝟐𝟗 ∗ 𝟏𝟎−𝟑 𝑳𝟑

−𝟏. 𝟓𝟎𝟓𝟖 ∗ 𝟏𝟎−𝟓 𝑳𝟑 − 𝟗. 𝟒 ∗ 𝟏𝟎−𝟓 𝑯
11. 𝐅𝐚 is the orifice thermal expansion factor.
 It is introduced to correct for the error resulting from expansion or contraction of
the orifice operating at temperature appreciably different from the temperature
at which the orifice was bored.
 𝑭𝒂 = 𝟏 + 𝟏. 𝟖 ∗ 𝟏𝟎−𝟓 (𝒕𝒇 − 𝒕𝒎 )
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 Where:
 𝒕𝒎 = temperature during orifice boring, ℉ . 𝒕𝒇 = fluid temperature, ℉