I am attempting to explain to my boss the dependency of gas composition to the transit time in ultrasonic meters. I am getting conflicting information of the dependency of the speed of sound in a gas with molecular weight. Some (reputable?) web sites show an equation with dependency on specific heat ratio and temperature only. Others show that there is a molecular weight dependency. Can anyone cite a reliable source of information? Thank You.
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Ultrasonic flow meter speed of sound in various gases.
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btrueblood
Mechanical
You don't have a copy of a thermodynamics text lying around?
The wikipedia article on speed of sound has a pretty decent writeup.
The wikipedia article on speed of sound has a pretty decent writeup.
OK, the speed of sound is calculated by:
v = (k*R[sub]gas[/sub]*T[sub]upstream[/sub])[sup]0.5[/sup]
The adiabatic constant is gas composition dependent. R[sub]gas[/sub] is the Universal gas constant divided by the gas' molecular weight which is very much composition dependent.
Pressure is not a factor. Density is not a factor. Sonic velocity is only a function of gas composition and upstream temperature.
[bold]David Simpson, PE[/bold]
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
v = (k*R[sub]gas[/sub]*T[sub]upstream[/sub])[sup]0.5[/sup]
The adiabatic constant is gas composition dependent. R[sub]gas[/sub] is the Universal gas constant divided by the gas' molecular weight which is very much composition dependent.
Pressure is not a factor. Density is not a factor. Sonic velocity is only a function of gas composition and upstream temperature.
[bold]David Simpson, PE[/bold]
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
georgeverghese
Chemical
A brief narrative on this topic may be found on page 6-22 of the 7th edn in Perry Chem Engg Handbook.
Here's a couple of paragraphs from Fundamentals of Multipath Ultrasonic flow meters for Gas Measurement on gas composition:
Gas Composition Effects
Sensitivity to gas composition is a bit more difficult to quantify as there is an infinite number of sample analyses to draw from. Let’s assume a typical Amarillo gas composition with about 90% Methane. If the chromatograph were in error on methane by 0.5%, and the remaining components were normalized to account for this error, the resulting effect on speed of sound would be 0.03%. Thus, minor errors in gas composition, for relatively lean samples, may not contribute significantly to the uncertainty.
However, let’s look at another example of a Gulf Coast gas with approximately 95% methane. Suppose the methane reading is low by 0.5%, and this time the propane reading was high by that amount, the error in computed speed of sound would be 0.67% (8.7 fps!). Years ago one could argue this may not be a “typical” error. However, with the recent introduction of shale gas and deep water gas into the mix this has become an increasing “typical” application.
There are many scenarios that can be discussed and each one would have a different effect on the result. The uncertainty that gas composition contributes to the speed of sound calculation remains the most elusive to quantify, and, depending upon gas composition, may prove to be the most significant.
A typical question is “what difference can be expected between that determined by the meter, and one computed by independent means?” It has been shown [Ref. 3] that the expected uncertainties (two standard deviations) in speed of sound, for a typical pipeline gas operating below 1,480 psig, are:
• ultrasonic flow meter measurement: ±0.17%
• Calculated (AGA 8): ±0.12%
Since the ultrasonic flow meter ’s output is independent of the calculation process, a root-mean-square (RMS) method can be used to determine the system uncertainty. Thus, when using lean natural gas below 1,480 psig, it is expected that 95% of readings agree within 0.21% (or about 2.7 fps). Therefore, it may be somewhat unrealistic to assume the meter will agree within 1 fps under typical operating conditions. Concluding this discussion on speed of sound, this “integral diagnostic” feature may be the most powerful tool for the technician. Using the meter’s individual path speed of sound output, and comparing it to not only the computed values, but also comparing within the meter itself, is a very important maintenance tool.
Caution should be taken when collecting the data to help minimize any uncertainty due to gas composition, pressure and temperature. Additionally, it is extremely important to obtain data only during periods of flow as temperature stratification can cause significant comparison errors. By developing a history of meter SOS, and comparing with computed values, it can also be used as a “health check” for the temperature measurement used to determine corrected volumes.
page 7, Link
Gas Composition Effects
Sensitivity to gas composition is a bit more difficult to quantify as there is an infinite number of sample analyses to draw from. Let’s assume a typical Amarillo gas composition with about 90% Methane. If the chromatograph were in error on methane by 0.5%, and the remaining components were normalized to account for this error, the resulting effect on speed of sound would be 0.03%. Thus, minor errors in gas composition, for relatively lean samples, may not contribute significantly to the uncertainty.
However, let’s look at another example of a Gulf Coast gas with approximately 95% methane. Suppose the methane reading is low by 0.5%, and this time the propane reading was high by that amount, the error in computed speed of sound would be 0.67% (8.7 fps!). Years ago one could argue this may not be a “typical” error. However, with the recent introduction of shale gas and deep water gas into the mix this has become an increasing “typical” application.
There are many scenarios that can be discussed and each one would have a different effect on the result. The uncertainty that gas composition contributes to the speed of sound calculation remains the most elusive to quantify, and, depending upon gas composition, may prove to be the most significant.
A typical question is “what difference can be expected between that determined by the meter, and one computed by independent means?” It has been shown [Ref. 3] that the expected uncertainties (two standard deviations) in speed of sound, for a typical pipeline gas operating below 1,480 psig, are:
• ultrasonic flow meter measurement: ±0.17%
• Calculated (AGA 8): ±0.12%
Since the ultrasonic flow meter ’s output is independent of the calculation process, a root-mean-square (RMS) method can be used to determine the system uncertainty. Thus, when using lean natural gas below 1,480 psig, it is expected that 95% of readings agree within 0.21% (or about 2.7 fps). Therefore, it may be somewhat unrealistic to assume the meter will agree within 1 fps under typical operating conditions. Concluding this discussion on speed of sound, this “integral diagnostic” feature may be the most powerful tool for the technician. Using the meter’s individual path speed of sound output, and comparing it to not only the computed values, but also comparing within the meter itself, is a very important maintenance tool.
Caution should be taken when collecting the data to help minimize any uncertainty due to gas composition, pressure and temperature. Additionally, it is extremely important to obtain data only during periods of flow as temperature stratification can cause significant comparison errors. By developing a history of meter SOS, and comparing with computed values, it can also be used as a “health check” for the temperature measurement used to determine corrected volumes.
page 7, Link
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