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Analysis of Temperature and Pressure Conditions on Flow Measurement

Introduction

Mass flow control for gases is a topic which has been studied and defined for several centuries – dating back to the 1600s. Given this level of time and attention, the principles behind mass flow are very well understood. Commercial methods for controlling and measuring mass and volumetric flow universally publish specifications which give prospective users the ability to accurately assess the suitability of the instrumentation for their requirements. Despite being straightforward theoretically, the ability to evaluate systems based on their published specifications can be confounded by several factors:

  • Differing levels of flow error inherent to a device under standard calibration and use conditions
  • Differences from the manufacturer’s standard calibration conditions and the conditions under which the mass flow measurement is actually made

In this analysis, we set out to make comparisons of mass flow accuracy using the published specifications of many commonly used mass flow devices and comparing them to Alicat’s MC models. We will first assess the error inherent in the flow measurement under standard calibration conditions. We then look at the effect of common flow control applications where the flow rate measurement may be affected by variances from the standard calibrated temperature and pressure. This involves a discussion of temperature and pressure coefficients and their effect on mass flow, an often overlooked topic, but one which can be critical for proper prediction of system performance.

Model comparison

Table 1: Published specifications and models for all of the devices used in this comparison. In the case of Alicat specifications we have measured and confirmed these specifications in our test lab. When specifications were unavailable, the space is crossed.

Comparison of Mass Flow Meters

We began by obtaining published specifications for mass flow instrumentation from various manufacturers. Our method was to compare devices from a wide range of manufacturers utilizing a variety of technologies, in order to obtain a comprehensive evaluation. The goal was to gain insight into the differences in accuracy between these devices. Note that in many cases, there are a very wide range of devices available from the same manufacturer - in some cases in excess of 6 units overlapping in features and function. For the purposes of clarity we chose the most accurate non-Coriolis device and utilized the best published specifications from each manufacturer. When a manufacturer offered a higher precision calibration option (often referred to as “high accuracy” or “high performance”) we utilized the specifications for that option. For Alicat devices, we used standard versions for these purposes; high accuracy versions would display even greater flow rate accuracy. Comparisons between

differing mass flow technologies and manufacturers are not necessarily readily available. There have, however, been a number of publications where existing MFCs are used a standard to compare against new processes or technologies (ref 3-5). Specifications between units are often expressed using different units and/or standard conditions. To facilitate comparison we converted all specifications to a standard format, based on commonly use units (°C and Pounds per Square Inch (psi)). All specifications used in this paper are summarized in Table 1.

The analysis carried out will be most useful when applied to a hypothetical device used in a wide range of conditions. For this scenario, we analyzed a 100 Sccm device flowing air under the manufacturer’s stated calibration conditions, one of the most common configurations that we see in use. Figure 1 shows a comparison of flow rate uncertainty (standard cubic centimeters per minute) for all of the

Flow rate comparison

meters analyzed at flow rates between 0 and 100 Sccm (full scale). We generated a flow model which takes into account the specifications given and calculates flow rate uncertainty at actual flow rates. In general, the flow rate uncertainty scales with flow rate. We make a more detailed explanation of the lower flow rates, where this is not necessarily the case, later on in this analysis. In Figure 1, lower values indicate that the unit is measuring with less uncertainty/more accuracy. The differences between specified mass flow error at the top and bottom of these accuracy graphs is large. The topmost graph in Figure 1, for example, specifies flow rate error of ±1 Sccm at 60 Sccm flow rate. The best specified meter demonstrates an error of ±0.35 Sccm, a 65% change in error between the two measurements.

Using the data presented one notices that several manufacturers’ devices (including Alicat) display a step change in error rates near the bottom of the flow range. As these graphs display uncertainty/error in flow rates, lower numbers indicate better performance. It’s noteworthy that in every case, Alicat’s Mass flow measurements are shown to be more accurate than other devices, displaying a lower flow uncertainty. At higher flows, Bronkhorst EL-Flow Prestige units are able to achieve similarly high levels of performance.

An interesting outcome from accurately measuring the flow rate error happens when looking at lower flow rates. This level of detail in measurement is carried out by Brooks Instruments and Alicat Scientific. At higher

flow rates, there are multiple sources contributing to the error in reading (including things like sensor noise, linearity, et cetera). However, below a certain point, the predominant noise factor becomes uncertainty in the zero point setting. As this error does not change with flow rate, it results in a straight line. While the actual flow rate uncertainty is invariant, the error still grows as a percentage of measure with increasing turndown. Table 2 shows how the percent error in reading will still grow at lower flow rates, despite the invariance of the error.

An extreme example can be seen by the comparison with the Sierra SmartTrak 100. For example, at a flow rate of 10 Sccm, the Alicat displays uncertainty of 0.1 cc. This means that actual flow at 10Sccm would range between 9.9–10.1 Sccm – a 1% error at a turndown of 10:1. The Sierra unit specifies a flow rate uncertainly of 1 Sccm, or 10 fold higher under the same conditions. Looking at only 1 Sccm, the Sierra now displays uncertainty equal to the measured value – 1 Sccm, ±1 Sccm (with the error equaling the flow rate). Even at a turndown of 100:1, the Alicat device would still produce a useful measurement: 1 Sccm ±0.1 Sccm.

The main takeaway is that most of these meters perform reasonably well in the middle or top of their flow range. But as turndown increases, the accuracy becomes much more important. As turndowns exceed 100:1, the usability of the measurements may be dramatically affected by the accuracy.

Uncertainty comparison charts
Uncertainty comparison table

Table 2 demonstrates this by comparing flow rate uncertainty at higher turndown (200:1) for the meters we compared.

Precise use cases always vary by application, but in most scenarios an error rate in excess of 20% means that the uncertainty can meet or exceed the actual flow. For example, at a calculated 40.5% error, and a flow rate of 0.5 Sccm, the Aalborg units can actually be flowing between 0.7025 to 0.2975 Sccm (at a desired flow rate of 0.5 Sccm).

Adding the pressure and temperature coefficients allows for a more real-world look at performance, since actual measurement conditions rarely match calibration conditions. For example, high pressure leak testing is a common application for flow and pressure meters and is carried out at pressures in excess of 100psi. Vacuum leak testing by comparison, is carried out down to 10-9 atm-cc/sec. Chemical engineering reactors can use hot gases, sometimes up to 100℃. High-temperature gases are also used in preform manufacturing and other applications requiring input compounds that are liquid or solid at room temperatures.

While the terms "pressure coefficient" and "temperature coefficient" are commonly used on the specification sheets, it is worth discussing their precise definitions.

Pressure coefficient is usually expressed as follows:

Pressure Coefficient

Temperature coefficient is usually expressed as follows:

Temperature Coefficient

The implication of this equation is that as temperature shifts away from the calibration conditions, error in reading increases. The temperature coefficient then, defines the increase in error due to temperature shift away from the standard temperature.

While units expressed differ, one example from the Alicat specification sheet reads:

Mass Flow Span Shift

The graphs shown in Figure 3 utilize a heat map to facilitate exploration of the additional effect of temperature and pressure on flow rate measurements. An analysis of these heat maps shows an increase in error happens at the extremes of temperature and pressure. As units are routinely calibrated at standard atmospheric pressure, but operated at much higher pressure, the Y axis is of

Heat maps hsowing Uncertainty in flow measurement for various manufacturers

potentially greater interest. These graphs also visually demonstrate that pressure has a much greater impact than temperature: as one approaches pressures of 150 psi for example, accuracy can drop off dramatically. This effect is noticeably more pronounced than at the extremes of temperature (−10 to 60° C). It’s noteworthy that some units (Such as the Brooks SLAMf) that perform adequately near calibration conditions, suffer greatly degraded performance at increased pressures and temperatures. Also noteworthy is the amount of change demonstrated by the Alicat mass flow meter under high pressure and temperature; even at the extremes,

the change in reading error remains well below 2% of reading. Put another way, an Alicat meter reading 50 Sccm under calibration conditions, would still read 50 ±2 Sccm at 0°C and 150 psig. This demonstrates the relative insensitivity of the Alicat units at the extremes of temperature and pressure.

As it is unusual to take the temperature and pressure coefficients into account, this should be sobering information for most users. It is not only the flow rate error under calibration conditions that matters – but the flow rate error at operating pressure and temperature conditions as well.

Conclusions

Modern mass flow meters and controllers offer unprecedented levels of accuracy and precision, even compared to devices from less than a decade ago. This is primarily due to advancements in sensing and signal processing technologies, which benefit mass flow measurement as a whole. All manufacturers listed do an admirable job of measuring and reporting the specifications for their various devices. In this white paper, we evaluated the results of a comparison between various mass flow control devices using their published specifications. These specifications are extensive enough to allow for predictions of measurement accuracy under various temperatures, pressures and flow rates.

When comparing Alicat’s differential pressure based mass flow measuring instruments to other technologies and systems, Alicat units generally specify better mass flow accuracy. This is despite using the best available units with the highest performing options from other manufacturers. Under certain conditions, some other meters can measure with accuracy close to the current Alicat flow meters. In no incidence, however, do competitors outperform the standard current model Alicat flow meters and controllers.

While comparisons are normally made under calibration conditions and flow rate errors calculated under these same conditions, we have taken the additional step of evaluating performance under temperature and pressures outside of these standard calibration conditions. These conditions differ from standard calibration conditions and are more likely to match those under which the flow measurement is actually performed. We presented this data utilizing heatmaps to facilitate visualization of the differences between units. Under these more realistic conditions, the gap in performance between Alicat meters and competitors widens even further.

This comparison set out to evaluate the accuracy of flow measurement for various mass flow meters. Using published specifications, the results show that Alicat manufactures the most accurate non-coriolis mass flow instruments currently available, under the conditions modeled. The authors hope that this comparison is useful and welcome commentary and discussion.