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  • By Michael Bess
  • Automation Basics

Instrument calibration should never be taken for granted, and thermal mass flowmeters are no exception. Flowmeters can be built with the highest safety ratings, features, and functions and the most industrially robust sensor technology, and still deliver unsatisfactory performance. This happens if the calibration is inaccurate or subject to uncertainty due to an equivalency-based calibration or simulation methods rather than an “actual” fluid calibration.

Poor calibration practices can result in possible safety exposures and process inefficiencies that might go undetected until the process is running and something goes wrong. Inefficient processes also frequently result in poor product quality and excessive costs, which negatively impact the bottom line and competitiveness.

Figure 1. Thermal dispersion principle of operation. Thermal mass flow sensors comprise two platinum resistance temperature detectors (RTDs) that are protected within thermowells. One RTD is heated while the other provides a reference by measuring the process temperature. This temperature differential is directly proportional to the mass flow measurement.

All thermal mass flowmeters work by measuring the cooling effect of a moving gas along a cylinder. The cooling effects are mostly a function of the properties of the gas, including its thermal conductivity, specific heat, density, and viscosity (figure 1). This is true for all thermal mass flowmeters, regardless of their measuring technique. Additional variations come from the sensors themselves and how each sensor is affected across its full flow range.

Heat transfer path variability

All thermal flowmeter manufacturers need to understand not only the heat input equation and the surface area, but all the heat transfer paths. The variability in the sum of these heat transfer paths will be unique to the flowmeter and may differ in the same way fingerprints differ on someone’s hands. Although the right index and left index fingers of your hands appear similar, they are actually different in their details. Similarly, the sensors of thermal mass flowmeters, even with tight manufacturing tolerance controls, precision methods of sensor fabrication, and the automation of sensor assembly, are subject to variations. These variations, even if subtle, make a formulary, standardizing gas correction factor inadequate and much more complex than a mere single variable correction factor.

Calibration laboratory

The capital investment and infrastructure needed to develop and maintain traceable, actual gas flow stands is substantial, particularly for gases that are hazardous or flammable. Additionally, flowing the specific gas itself, plus the energy required to flow it at specific temperature and pressure conditions, comes at a higher recurring cost. Many thermal mass flowmeter manufacturers simply sidestep this investment and evade the higher cost of an actual gas calibration by performing a simulated or “equivalency” quasi-calibration.

Not all “equivalencies” equal

Manufacturers performing equivalency calibrations use a reference or surrogate fluid, typically air, at ambient conditions. They apply empirically based calibration parameters that use a theoretical, formula-based calculation to the air flow readings to set their instrument’s gas calibration. At best, this procedure simply infers the fluid’s cooling effects on the gas properties such as viscosity, density, specific heat, thermal conductivity, and Reynolds number ranges.

Unlike an actual gas calibration, this inferred equivalency method does not accurately replicate the true thermal heat dissipation of the actual gas. Corrections required for process conditions, such as variations of pressure and temperature extremes, create an even greater uncertainty. As stated and confirmed by ISO Standard 14511, Section 8, “... the best practice for calibrating thermal mass flowmeters is to perform an actual gas calibration, and at actual process conditions, when feasible.”

For any critical application where stoichiometric calculations are critical or when measured gas flow rates are essential for safety or efficiency, no simulated calibration method should be considered for thermal flowmeters when an actual, “true” fluid calibration is available.

Furthermore, an air equivalency, simulated calibration is not recommended where process conditions are moderately unstable, where flow velocity profiles are potentially in the transitional range, or where there is a potential nonlinear relationship between the calibration fluid and the actual service fluid. Therefore, theoretical or equivalency calibrations represent a very limited range of applications. Many flow ranges with turndowns greater than 10:1 extend well beyond a simple linear correction range, and a single factor correction as applied by many manufacturers is ineffective due to the nonlinear relationships between the fluids. This is particularly true with thermal mass flowmeters that rely on thermal conductivity and cooling effects as the essential measurement.

Problem with simulated calibrations

To illustrate graphically the measurement uncertainty of simulated calibrations, consider the accuracy performance curves in figure 2. These curves were obtained from a thermal flowmeter produced by a global, multitechnology flowmeter manufacturer, whose meter embedded a user-selectable menu of gases. It is alarming to see the extent of the errors. Clearly, this instrument is not calibrated directly in each of these basic gas compositions but instead applies an inaccurate equivalency algorithm correction factor.

Figure 2. Brand X thermal mass flowmeter accuracy performance using selectable gas menu, equivalency (4-inch line size, 4–20 mA output signal converted to SFPS at 70°F [21°C]). Calibrated range of unit is 10-692,8 SFPS in air.

The large errors seem to indicate a simple, single order correction, and the manufacturer does not even attempt to use a polynomial correction for purposes of correcting nonlinearities. Through most of the flow range you can see that these corrections, while extremely large in scale, have a certain linearity. As expected, the air and nitrogen curves are relatively close to zero offset, because the base calibration is performed in air as the calibration fluid. However, when the instrument has one of the other gases selected, then the additional measurement error after the theoretical correction factor is applied can be as high as ±100 percent!

Also detectable is the inability of the algorithm to correct nonlinearity for some gases flowing at slightly elevated temperatures. This nonlinearity range can vary as much as 30 percent, which means a correction factor approach, even if accurate, would not apply across the full fluid flow range.

Ask about procedures

To demonstrate the significant performance improvement obtained by using an actual gas calibration, refer to figure 3, which shows an FCI Model ST100 using an actual gas calibration for natural gas. Compare this result with the natural gas plot line in figure 2, which used an equivalency calibration. The resulting improvement is exceptional.

Figure 3. FCI Model ST100 thermal mass flowmeter accuracy performance in natural gas using actual calibration (4-inch line size, 4–20 mA output signal converted to SFPS, at 70°F [21°C])

If you are responsible for flowmeter performance in critical processes, or for plant safety or environmental compliance, then you have a right to ask manufacturers about their calibration procedures. They should be able to explain and demonstrate how your company’s new meters are to be calibrated, on what types of traceable equipment, under what methods and what conditions, and to which specific mechanical, electrical, and safety standards.

You should ask to tour the calibration laboratory where the work will be performed and to meet with the engineers and technicians responsible for the work. In addition, a flowmeter factory representative should be made available to you when necessary to review the application requirements and inspect the actual meter location to ensure a successful installation.

This article originally appeared in FCI’s Air/Gas Flow Measurement Solutions Handbook (https://www.automation.com/en-us/products/forms/air-gas-flow-measurement-solutions-handbook).

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About The Authors


Michael Bess is calibration lab and test engineering manager for Fluid Components International (FCI), www.FluidComponents.com. FCI has invested in and maintains more than 20 calibration rigs on three continents. These flow stands, in various pipe diameters, can flow air, pure inert gases, hydrocarbon gases, and precision mixed-gas compositions with up to 20 actual gas constituents.