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What Is The Point Of An Accuracy Statement

Manufacturers provide datasheets or specification sheets for the flow measuring devices they supply and whilst all are created with the best of intensions, they are sometimes difficult to decipher and almost always difficult to compare.

In an ideal world there would be a standard method for declaring “accuracy” however in reality this is not always possible. There are so many variables that could influence a sensor and its measurements that the methodology would run the length of a page plus of course not every variable is applicable to every sensor. Furthermore, a manufacturers specification sheet is often used as a sales brochure so it might not be in their interest to include all relevant data.

Could we benefit from a "measurement uncertainty" value?

Perhaps what manufacturers should state is the measurement uncertainty of their device at specified conditions? This could certainly be a good step forward but is this single value sufficient enough? In the case of traditional mass flow measurement this uncertainty would need to be stated for each point from full flow all the way down the flow curve until that sensor reaches its bottom limit. In addition, the gas type being measured would need to be included in any calculations. In the case of Alicat mass flow meters/controllers these two statements do not apply as the stated accuracy covers everything – but more of that later.

The Definition of Accuracy

So, what is accuracy? The internet tells us that it is “the degree to which the result of a measurement, calculation, or specification conforms to the correct value or a standard”. In terms of weight, any measurement in kilograms would be compared to the national kilogram at NPL, Teddington or ultimately to the world kilogram held at Pavillon de Breteuil, Paris. In terms of mass flow, a measurement is compared to a standard that is traceable back to a National body such as UKAS or NIST. Of course, direct comparison to these national (and international) weights and measures is not possible so Transfer Standards are employed. Referring once again to mass flow, it is interesting that Laminar Flow Elements are most commonly used as Transfer Standards as they are deemed to be least affected by external influences and hence most accurate. The Alicat meters mentioned later utilize a Laminar Flow Element as their measurement technology.

Is the above definition what the user means by “accuracy”? If the user requires empirical data, then yes. A chemist might wish to combine two Hydrogen atoms with one of Oxygen and they need that to be exact - add an extra Oxygen and the result will not be water! If however we take a different user, perhaps a flavoured water manufacturer, then they need to dose exactly the same amount of flavouring batch after batch so that they all look and taste the same. They therefore want the measurement to be repeatable; not exactly a precise value but whatever it is it must be the same time after time. This is not accuracy, this is Repeatability. If we now take this same drinks manufacturer and look at their second production line we can see that the process is the same and all the sensors are the same. The concern here is that all the measurements should be the same across both production lines. Again, this is not accuracy, this is Reproducibility. We can therefore see that the formal description of accuracy does not fit into the real world and should be more like “the degree to which the result of a measurement, calculation, or specification conforms to what the user wants it to be”. The important question to consider is therefore “what accuracy is wanted, and why”.

What Affects Accuracy?

Continuing with the theme of mass flow measurement and returning to an empirical meaning of accuracy, there are physical factors that impact on sensor readings. Commonly these factors are listed within a datasheet but sometimes they are only mentioned with Operating and Maintenance Manuals. These factors are: temperature effects, pressure effects, attitude effects, conversion factor error and linearity. A comparison of typical values between mass flow measurement techniques can be seen within the following table:

Manufacturer / Model / Measurement TechniqueAlicat M-Series with LFE/DP SensorAlicat CODA CoriolisBy-Pass ThermalChip-Flow Thermal
Accuracy Statement0.6% Rg or 0.1% FS0.5% Rg or 0.05% FS0.5% Rg + 0.1% FS1.5% Rg + 0.5% FS
Temperature Effects on Span0.01% Rg / C0.005% Rg / C0.05% Rg /C0.2% Rg / C
Pressure Effects0.1% Rg / BarNil0.1% Rg / BarNil
Attitude EffectsNilNil0.2% Rg0.0001% Rg
CF ErrorNilNilGas DependentActual Gas Only
Repeatability0.1% Rg + 0.02% FS0.05% Rg or 0.025% FS0.2% Rg0.5% Rg

As a starting point the following graph compares the four measurement techniques in terms of total measured error as a percentage of reading. For simplicity the actual plus/minus error is charted as the positive error only.

Graph compares the four measurement techniques in terms of total measured error as a percentage of reading

From the above it can be seen that;

  1. The laminar flow element / differential pressure sensor performs well across the full flow regime. Even at 1/500 of the full scale the total error is only +/- 2.7% of reading after Tare.
  2. The CODA Coriolis sensor out-performs the LFE/DP sensor at higher flows. It is only when the percent of full-scale calculation takes precedence that the error starts to increase.
  3. Both thermal sensors show both increased error and the classic “trumpet shape” error band due to the percent of full-scale calculation. Their low flow capability is also cut off at the 50:1 turndown point.

To illustrate the impact of specifications we can now look at changing the gas type to Argon and Propane whilst increasing the pressure and temperature:

Changing the gas type to Argon and Propane whilst increasing the pressure and temperature

The Alicat M-Series is not effected by the change in gas and as the sensor measures both the static pressure and the temperature these factors are eliminated. Similarly, the Coriolis sensor is unaffected by process condition changes. The by-pass thermal is adversely affected by the presence of the conversion factor whereas the chip-flow sensor is sensitive to temperature. It is assumed that the chip sensor is calibrated to the actual gas being used.

This final graph further illustrates the impact of conversion factors on the thermal bypass sensor.

The impact of conversion factors on the thermal bypass sensor

What Really Matters in the Real World?

It is clear that comparing and including all sources of error is important. A statement on “accuracy” does not always give the full picture.

However, the actual accuracy only needs to conform to what the user wants it to be which can also be extended to “the choice of instrument depends largely upon the needs of the application” rather than the comparison of datasheet specifications. Chip-sensor flow devices find their niche within miniature systems where space is limited. By-pass thermal devices are strong within high-pressure systems and/or where ultra-aggressive gases are present. Laminar flow element/DP sensors can be seen to have high levels of performance across virtually all other applications especially where high turndown, good accuracy and cost-effective solutions are required. Interestingly the Alicat CODA Coriolis Series – especially in low cost OEM format – pretty much trumps all. It has a small footprint, meets the needs of aggressive gases, has a high pressure capability and is unaffected by changes in the process. No wonder Coriolis is commonly referred to as “the almost perfect sensor for flow measurement”.

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