Mass flow meter for a gas mixture with a changing composition
How do you measure accurately when the composition is constantly changing?
Using a mass flow meter for a gas mixture whose composition changes continuously is technically demanding. The first thought might be a thermal flow meter. For capillary models, gas corrections are possible with linear correction factors (K-factors), but these are not very accurate in practice: they assume a linear relationship in the gas mass, while in reality temperature and pressure make this multidimensional. A second option is a MEMS thermal flow meter with a separate correction curve applied for each gas mixture, but that is costly because of the large number of calibrations.
Alternatively, a differential pressure meter with a laminar flow element is an attractive solution. The only gas variable is then the viscosity. By simultaneously measuring the temperature and absolute pressure accurately, the viscosity and density of the gas can be calculated accurately under all conditions. These values can all be found in the extensive NIST gas database (REFPROP).
⏱ approx. 7 minutes reading time
The problem: a varying gas mixture has a variable viscosity
The Vögtlin d-flux is a laminar differential pressure mass flow meter. Its operating principle is based on placing a Laminar Flow Element (LFE) in the gas path: a structure that converts turbulent inflow into laminar flow. As described by the Hagen-Poiseuille law, the pressure drop across the LFE depends solely on the viscosity of the gas. A differential pressure sensor measures that pressure difference; an absolute pressure sensor and a temperature sensor measure the process conditions. The microprocessor calculates the actual viscosity and density and combines these calculated variables into an accurate gas mass flow.
Because viscosity is the only gas-dependent variable in the measurement equation, the d-flux internally calculates the viscosity value for each configured gas based on the current pressure and temperature. This can be imagined as a multidimensional table: for a given gas, pressure and temperature together determine the viscosity value used in the flow calculation. This allows the mass flow meter to switch gases without being reconfigured while maintaining accuracy, provided the gas matches the programmed gas.
With a gas mixture of CO₂ and air, the composition adds a third dimension to that viscosity model. The viscosity then depends not only on pressure and temperature, but also on the current mixing ratio. A mixture of 20% CO₂ has a different viscosity from a mixture of 80% CO₂, and these values are far enough apart to cause a significant measurement error if the mass flow meter is configured for the wrong mixing ratio.
At room temperature, air has a dynamic viscosity of approx. 18.5 µPa·s. CO₂ is considerably lower: around 15.0 µPa·s, a difference of almost 20%. With a changing mixing ratio, the effective viscosity of the gas mixture shifts continuously, and with it the outcome of the measurement calculation if the meter is set to a single fixed mixing ratio.
| Gas / mixture | Viscosity (µPa·s, 20°C) | Relative to air |
| Air | 18,5 | Reference |
| CO2 | 15,0 | −19% |
| 20% CO2 / 80% air | ~17,8 | −4% |
| 50% CO2 / 50% air | ~16,8 | −9% |
| 80% CO2 / 20% air | ~15,7 | −15% |
A mass flow meter configured for pure air that then measures a mixture of 80% CO₂ and 20% air introduces a systematic error. This is not noise but a structural shift: the meter measures the correct pressure, temperature and differential pressure, but the calculation is based on the wrong gas composition. The measured value looks correct but is not.
Why a standard mass flow meter falls short here
The d-flux can measure a stable gas or a stable gas mixture accurately with a single configured gas profile, because the viscosity value is determined internally based on the measured pressure and temperature. This works very well as long as the gas composition does not change.
With a continuously changing CO₂/air gas mixture, however, a third dimension is missing from that calculation: the composition itself. The mass flow meter knows the pressure and temperature at any moment, but not what percentage of CO₂ the gas contains at that moment. The viscosity value the meter uses for its calculation is therefore always that of a single fixed configured mixing ratio, even if the actual mixing ratio is different at that moment.
The result is a systematic measurement error proportional to the viscosity difference between the configured and the actual mixing ratio. This error is not visible in the measurement signal itself: the meter gives a number, but that number is wrong.
If you measure the current composition of the gas mixture externally with a CO₂ percentage meter and pass that information to the d-flux, you fill in the missing dimension. The mass flow meter can then use the correct viscosity value for each known mixing ratio. That is exactly what the profile system does in combination with the PLC: the composition is determined externally and the meter switches to the profile with the correct viscosity curve for that ratio.
The solution: multiple programmed gases and a PLC connection
The customer in this case had a gas stream in which the CO₂ content changed continuously as a result of their production process. The composition was variable at any moment but measurable: the customer had a CO₂ percentage meter that sent the current CO₂ content to the PLC.
The solution made use of the d-flux's ability to store multiple programmed gases. Instead of one configuration for the entire gas mixture, several mixing ratios were programmed separately and stored as separate profiles in the mass flow meter, such as profiles for 20% CO₂/80% air, 30% CO₂/70% air, 40% CO₂/60% air and so on, in steps of, for example, 10 percentage points.
The PLC received the current CO₂ content from the percentage meter, used it to determine which programmed gas profile was closest to the current mixing ratio and selected that profile in the d-flux via Modbus or an Ethernet protocol. The mass flow meter automatically switched to the matching profile and then measured the flow with the correct configuration for that specific mixing ratio.
Each profile also has its own totaliser, so that the cumulative flow per mixing ratio can be tracked separately. This is useful for mass balance calculations in which the quantities of CO₂ and air must be processed separately.
The step size determines the remaining measurement error between two gas profiles. With steps of 20 percentage points, the maximum mixing ratio deviation is 10 percentage points from the nearest profile. With steps of 10 percentage points, that deviation drops to 5 percentage points. The d-flux has room for up to 15 programmed gases, which allows steps of approx. 7 percentage points over a range of 0% to 100% CO₂.
This solution not only offers excellent accuracy, but is also economically attractive. In addition to mass flow, the multiparameter d-flux also provides pressure, temperature and a volume totaliser. Configuration is easy via Bluetooth, and diagnostics can be performed in the same way. Together with the excellent long-term stability and the wide dynamic range, this results in a low total cost of ownership.
In addition to the mass flow meter (MFM) version, the d-flux is also available as a mass flow controller (MFC) with an integrated proportional control valve. Contact Inacom for more information.
Practical considerations for implementation
Step size of the profiles
The more programmed gases are configured, the smaller the maximum deviation between the current mixing ratio and the selected profile. With 15 profiles distributed over a range of 0% to 100% CO2, steps of approx. 7 percentage points are achievable. In most industrial applications, a remaining deviation of a few percentage points in the mixing ratio is acceptable: the contribution to the total measurement uncertainty then remains smaller than the basic accuracy of the meter itself.
System response time
The total response time of the signal chain consists of three components: the response time of the CO2 analyser, the processing time of the PLC and the switching time of the d-flux profile. The d-flux itself responds within 120 msec. If the mixing ratio changes quickly, within seconds, the CO2 analyser must be fast enough to select the right profile in time. If the mixing ratio changes slowly, over minutes, the response time places virtually no demands.
Programming the gases
The gas profiles are programmed by Vögtlin Instruments for the specified mixing ratios. This means that the desired mixing ratios are specified when ordering. Changes afterwards are possible but require reprogramming. It is therefore wise to map out the most common mixing ratios in the process carefully before ordering the meter. Inacom is happy to think along about the optimal profile division during the specification phase.
Dryness of the gas
The d-flux is only suitable for dry and clean gases. If the gas stream contains moisture or particles, gas conditioning upstream of the meter is necessary. Otherwise, the LFE may become clogged, which affects the pressure and makes measurements inaccurate. CO2-rich gas streams are humid in some processes, such as fermentation processes or combustion gases. In those cases, a Nafion dryer or condensate trap upstream is a requirement before the gas reaches the d-flux.
