The Effect of Temperature and Pressure on Flow Measurement
Mic Chaudoir, Ph.D. Kevin Gudenkauf, MSc
|2 of 12ALICAT.COMThe Effect of Temperature and Pressure on Flow MeasurementMic Chaudoir, Ph.D.Market Managermchaudoir@alicat.comDr. Chaudoir obtained his degree in Cell and Molecular Biology from Northwestern University in 1997.He has led product development and marketing at a number of scientific instru- ment companies including Leica Microsys- tems, Photometrics and Fiberguide Indus- tries. He joined Alicat Scientific in late 2018 and currently leads Alicat’s efforts in the bioreactor and optics markets.Kevin Gudenkauf, MScTest EngineerKevin@alicat.comMr. Gudenkauf obtained his Bachelor’s of Science in Physics from the University of Arizona. He went on to obtain his Masters of science in Physics from The Ohio State University in 2012. He has since helped advance Alicat’s differential pressure tech- nology and has held positions in applica- tions engineering and test engineering. His latest projects include testing and validation of Alicat’s industrial protocols and refinements to the Alicat flow mea- surement models for improved accuracy and reliability.|
|Analysis of Temperature and Pressure Conditions on Flow MeasurementMass flow measurements have achieved never before seen levels of accuracy and precision. But how do you know what level of precision you need? And further, how does this information relate to your unique application or system? This white paper gives a comprehensive overview and comparison between mass flow meters representing a variety of manufacturers and technolo- gies. This information will equip you to make the most of your existing instruments and intelligently evaluate new instrumentation for your particular system. Get the latest information on why specifications matter and what impact this will have on your mass flow measurements!The Effect of Temperature and Pressure on Flow Measurement ALICAT.COM 3 of 12|
Mass flow control for gases is a topic which has been studied and defined for several centuries –dating back to the 1600s.1 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 re- quirements. 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 cali-bration conditions and the conditions under which the mass flow measurement is actually madeIn this analysis, we set out to make comparisons of mass flow accuracy using the published specifications of many commonly used mass flow devices and com- paring them to Alicat’s MC models. We will first assess the error inherent in the flow measurement under stan- dard 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 coeffi- cients and their effect on mass flow, an often overlooked topic, but one which can be critical for proper prediction of system performance.1 “Gases and Gas Laws/Boyle’s Law Lab.” Wikiversity, en.wikiversity.org/wiki/Gases_and_gas_laws/Boyle’s_law_lab.
Apparatus for transference of gases and pressure gauge Credit: Wellcome Collection
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|Accuracy (% Full Scale)||0.1||0.2||0.2||0.1||0.18||0.35||0.2||1.0||0.3|
|% Reading 0.6 0.5 1.0 0.5 0.9 1.0 0.5 0.5|
|Repeatability (% Full Scale) 0.02 0.2 0.01 0.04 0.2 0.2 0.2|
|Temp coefficient (% Full Scale) 0.01 0.05 0.3 0.02 0.05 0.04 0.05 0.025|
|% Reading (per °C)||0.01||1.0||0.025||0.1||0.08|
|Pressure coeffient % Full Scale 0.00068 0.01 0.2 0.0 0.01|
|% Reading (per PSI)||0.0068||0.2||0.0103||0.03||0.03||0.02||0.0138|
|Stated Controllable Range 10,000 200 1,000 150 100 50 50 50 100Table 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 MetersWe began by obtaining published specifications for mass flow instrumentation from various manufacturers.2 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 be- tween 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 rate2 See appendix for the actual datasheets used.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 fa- cilitate 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 ap- plied 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 con- figurations that we see in use.Figure 1 shows a comparison of flow rate uncertaintyThe Effect of Temperature and Pressure on Flow MeasurementALICAT.COM 5 of 12|
MFM 2120 RS-232 low flow
Red-Y High Performance
|(standard cubic centimeters per minute) for all of the 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 notewor- thy 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, Brokhurst 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 outby 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 dra- matically affected by the accuracy.6 of 12 ALICAT.COMThe Effect of Temperature and Pressure on Flow Measurement|
Figure 1: Uncertainty Comparison: Flow Rate Error vs. Flow Rate for 100 sccm MFCs 1.4
1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Figure 2: Percent Uncertainty vs. Flow Rate for Alicat 100 sccm MFCs 12
10 8 6 4 2 0
Sierra SmarttraK BrookS G40 axetriS mFm 2120 MkS mF1
aalBorg dPc 17 BrookS SlamF BronkhorSt el-FloW alicat m
0 20 40 60 80 100
Flow rate in Sccm
0 20 40 60 80 100
Flow rate in Sccm
The Effect of Temperature and Pressure on Flow Measurement ALICAT.COM 7 of 12
Percent uncertainty Uncertainty in Sccm
|Brand & Model||Uncertainty at 200:1 turndown (0.5 SccM) in SccM per % of measured flow|
|Alicat M||0.1 SCCM per 20% of measured flow|
|Bronkhorst EL-Flow Prestige 0.1025 SCCM per 20.5% of measured flow|
|Brooks SLAMf||0.18 SCCM per 36% of measured flow|
|MKS MF1 0.2025 SCCM per 40% of measured flow|
|Aalborg DPC 17||0.2025 SCCM per 40.5% of measured flow|
|Axetris MFM 0.205 SCCM per 41% of measured flow|
|Voegtlin Red-Y||0.3025 SCCM per 60.5% of measured flow|
|Brooks GF40 0.355 SCCM per 71% of measured flow|
|Sierra SmartTrak 100||0.5 SCCM per 100% of measured flow|
|Table 2: Comparison of flow rate uncertainty at 200:1 turndown on a 100SCCM flow meter.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 10-9atm-cc/sec. Chemical engineering reactors can use hot gases, sometimes up to 100 ̊C. 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 “tempera- ture coefficient” are commonly used on the specification sheets, it is worth discussing their precise definitions.Pressure coefficient is usually expressed as follows:Mass Flow Span Shift =∆% Reading(1 atmosphere + ∆ atmospheres)Temperature coefficient is usually expressed as follows:Mass Flow Span Shift = ∆% Reading (25°C + ∆ Temperature in °C)The implication of this equation is that as tempera- ture 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: ±0.01% Reading per °C from 25°CThe graphs shown in Figure 3 utilize a heat map to fa- cilitate 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 of8 of 12 ALICAT.COMThe Effect of Temperature and Pressure on Flow Measurement|
Figure 3: Heat Maps Showing Uncertainty in Flow Measurement for Various Manufacturers
160 Aalborg DPC
140 120 100
80 60 40 20
Axetris MFM 2120 160
140 120 100 80 60 40 20
Sierra SmartTrak 100
120 100 80 60 40 20
120 100 80 60 40 20
160 140 120 100
80 60 40 20
160 140 120 100 80 60 40 20 0
0 Vogtlin Red-Y High Performance 0
-10 0 10 20 30 40 50 60 -10 0 10 20 30 40 50 60 -10 0 10 20 30 40 50 60
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 pres- sure 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.
The Effect of Temperature and Pressure on Flow Measurement
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† We were unable to obtain complete published specifications for the Brooks GF40.
Uncertainty in percent at 100 Sccm Pressure (0–160 PSIG)
Modern mass flow meters and controllers offer unprece- dented 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 technol- ogies, 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 compari- son 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. Un- der 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.
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The Alicat 1-SLPM meter
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