Thermal mass flowmeters: when is pressure compensation important?

The claim that thermal mass flowmetering is independent of pressure is only half of the truth.

A frequently asked question by users is: “When is it necessary to use pressure compensation for a thermal mass flowmeter?” If you have spent any time searching the internet for thermal flowmeter suppliers, what you may have noticed is that many of them promote the thermal mass flow measuring principle as a “pressure- and temperature-independent” principle. Most of the time there is no explanation as to why this is the case, but if you search long enough you may come across such an explanation as offered by Sage Metering, Inc.:

“A thermal mass flow meter is a precision instrument that measures gas mass flow … These meters measure the heat transfer as the gas flows past a heated surface. The gas molecules create the heat transfer, the greater the number of gas molecules in contact with the heated surface the greater the heat transfer. Thus, this method of flow measurement is dependent only on the number of gas molecules and is independent of the gas pressure and gas temperature.”¹

Of course, what this is saying is that because thermal mass flowmeters measure mass directly, instead of deriving the measurement from volume flow, there is consequently no need to compensate for pressure or temperature as would be the case with other gas flow measuring principles like differential pressure, turbine, positive displacement and vortex shedding.

If you search longer, you might even come up with an explanation of why thermal mass flowmeters measure mass ‘directly’. For example:

“Thermal dispersion mass flowmeters measure the heat convectively transferred from the heated velocity sensor to the gas molecules passing through the viscous boundary layer surrounding the sensor’s heated cylindrical surface. Since the molecules bear the mass of the gas, thermal dispersion flowmeters directly measure mass flow rate.”²

Of course, this leaves out the whole thermodynamic explanation, but at least ties the heat transfer to the mass of molecules.

If you search even further, you may find a theoretical explanation like the following that proves the direct mass measurement using a theoretical explanation with formulas:

“The primary desired output variable is the total mass flow rate q_m flowing through conduit or flow body. q_m depends on the product ρV, the fluid’s mass density times the point velocity, embodied in the Reynolds number Re= ρVDμ. ρV is often called the ‘mass velocity’ and is the total mass flow rate per unit area (kgs∙m²).”³

The above explanation suggests that because one is actually solving for the product, ρV, which is contained in the Reynolds number, by equating it to other known terms in an empirical correlation — density itself is not a required term to solve for this product. Therefore, density does not have an influence on the solution of this product. That is, the mass velocity, which is being sought. Ergo, thermal mass measurement is not affected by density, and by matter of consequence, it is not affected by pressure and temperature.

However, when you continue searching the internet for thermal mass flowmeter suppliers you will come across statements such as, “Our meters are temperature-compensated”, or you might even happen upon some suppliers who offer a “pressure measurement” option. If you read further, you may find out that this pressure measurement option is also intended for compensating for changes in pressure. Now, you may already be asking yourself: “I thought that thermal mass flowmeters are pressure and temperature independent?”

Well, the truth is that this statement is only half of the truth. Thermal mass flowmeters are not dependent on density for the direct measurement of mass flow due to the reasons already stated above. However, they are greatly dependent on the fluid characteristics, which are in turn dependent on the gas composition, and the fluid characteristics (thermal conductivity λ, specific heat capacity c_p and dynamic viscosity μ) are all influenced by changes in pressure and temperature. As soon as the application conditions vary from the reference conditions (those laboratory conditions existing during calibration), then, without temperature and pressure compensation, there are additional measurement errors that must be considered. So, to say that thermal mass flowmeters do not require pressure and temperature compensation is an untruth. They do require it, and practically every thermal mass flowmeter manufacturer uses some form of compensation to do this.

Temperature has typically a much larger influence on the fluid characteristics than pressure does. Because the entire measuring principle is based upon temperature measurement, a dynamic correction of this is possible. Pressure usually has a lesser influence on the fluid characteristics, and typically a fixed pressure value is entered into the device during commissioning. If the process pressure changes, the fixed value in the device does not change with it. In effect, these devices are not corrected for changes in pressure.

Some devices allow for an input reading from a separately installed pressure transmitter. This enables a dynamic compensation for changes in pressure. However, when would such a compensation be necessary? Obviously, this requires a pressure measuring point, which may not always be available, and either a current input or bus communication. In the end, this could result in an increased measuring point price for the user, who is not always prepared to accept this especially when there are uncertainties about the added benefits.

As stated, pressure has typically a lesser influence on gas characteristics than temperature. However, its influence is also gas dependent and can be greater depending on the type of gas. Generally, we state that one can expect in air about ±0.25% o.r. additional error for every bar difference (in either direction) to the reference pressure (in this case, the static pressure entered into the device). On the other hand, certain gases like CO₂ or O₃ have a much larger dependency on the pressure, and the additional error can therefore be much higher.

The extent of influence of gas characteristics on the mass flow accuracy depends on thermal conductivity (being the largest factor), followed by specific heat capacity and then viscosity. For gases such as H and He the total error can be as low as 0.3–0.4% per bar pressure change, but for gases like CO₂ and O₃, the error can be as much as 0.85% or 0.88% per bar pressure change respectively. Therefore, users might need to make more serious consideration of pressure compensation for these gases.

Conclusion

Of course, gas characteristics alone should not be the sole determinant when deciding for or against pressure compensation. Other important factors should be the amount of pressure fluctuation in the application. If the pressure is deemed to be fairly constant, using pressure compensation could be simply overkill. If, on the other hand, the pressure is known to be unstable and to fluctuate by relatively large amounts, then it might be beneficial to use pressure compensation, especially in the case of gases like CO₂ whose gas characteristics are known to be more dependent upon pressure.

Lastly, perhaps the most important factor in deciding to use pressure compensation is to be candid about the importance of measuring accuracy and repeatability. Is a high level of measuring performance required for the application? Depending on the amount of pressure change, the corresponding measurement error might still be in an acceptable range for certain applications.

^{1. Whorff F 2023, Fundamentals of Thermal Mass Flow Measurement, Sage Metering, <<https://sagemetering.com/back-to-basics/fundamentals-of-thermal-mass-flow-measurement/>>}

^{2. Olin J G 2008, A Standard for Users and Manufacturers of Thermal Dispersion Mass Flow Meters, Sierra Instruments, p. 13 <<https://www.sierrainstruments.com/prnews/Thermal%20Mass%20Flow%20Measurement%20of%20Fluid%2010.15.08.pdf>>}

^{3. ibid., p. 17}

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