- Email: [email protected]
INRIM primary standard for microgas-flow measurements with reference to atmospheric pressure
Measurement 45 (2012) 2459–2463
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
INRIM primary standard for microgas-flow measurements with reference to atmospheric pressure Mercede Bergoglio, Domenico Mari ⇑ Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy
a r t i c l e
i n f o
Article history: Available online 15 November 2011 Keywords: Gas flow Primary standard Reference leak
a b s t r a c t Primary standard flowmeters are developed for the calibration of leak devices used in many applications in which is necessary to detect and quantify gas leakage from a material, a component or a system. At INRIM, a primary standard was designed and realized for the measurement of molar gas flow from 4 1010 mol/s to 2 107 mol/s with reference to atmospheric pressure. It is based on the constant-pressure–variable-volume method and is able to work with any tracer gas. The paper describes the primary standard, the mathematical model adopted for the estimate of the measurand and the uncertainty evaluation. The recent developments of the system, performed to improve the accuracy of the standard, are presented. The new layout of the flowmeter has allowed a study of the temperature effects on the gas flow measurements in the range between 15 °C and 30 °C. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Leak detection techniques [1] are applied in many fields of science and technology to verify if an object under control satisfies the required limits by a scientific study or prescribed specifications. Leak detectors are instruments for leak testing of materials, components, systems and they are periodically calibrated by leak devices, which are widely used secondary standards of gas flow. Primary standard micro-gas flowmeters have been developed to ensure traceability for gas flow measurements and provide system capable to generate and measure primary standard gas flows for the calibration of leak devices [2–6] or to be used in conjunction with continuous expansion systems [7,8]. In the last years many applications and instruments, in which leak testing is carried out with reference to atmospheric pressure, have been developed. Recently, National Metrological Institutes have realized primary standards [9–11] for the gas flow measurements with outlet to atmospheric pressure in order to provide the necessary support ⇑ Corresponding author. E-mail address: [email protected] (D. Mari). 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.10.039
for a correct traceability chain in this new flow metrology field, related to micro-gas flowing to the atmosphere. The paper describes the primary standard flowmeter designed, realized and recently improved at INRIM for the measurement of molar gas flow with reference to atmospheric pressure. It is based on the constant-pressure–variable-volume method and is able to work with any tracer gas, between 4 1010 mol/s and 2 107 mol/s with a relative standard uncertainty ranging from 4.6 102 to 0.4 102. In the last part of the paper, the temperature dependence of gas flow delivered by a capillary leak, calibrated by the primary standard flowmeter, is studied in the range between 15 °C and 30 °C. The results provide an experimental determination of the capillary thermal coefficient for different gases to take into account the influence of temperature when the measurements are performed with reference to atmosphere. 2. Description of the system and measurement procedure The quantity generated by a leak device and measured by a primary standard is the molar gas flow, which can
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be defined as the number of gas moles coming out from the leak per unit time. The INRIM primary standard flowmeter is based on constant-pressure and variable-volume method and it can measure molar flow rate in the range between from 4 1010 mol/s to 2 107 mol/s with reference to atmospheric pressure. Fig. 1 shows the scheme of the system: at the beginning of operation the reference and measurement volumes VR and VM are maintained at the same atmospheric reference pressure patm with valves V1, V2 and V3 opened and the three-way valve closed to the system and opened to air, in order to channel the gas flowing out from the device towards the air and avoid a strong accumulation of gas inside the leak. After the closing of valve V2, to eliminate eventual influence of reference pressure variations in VR, the valve V3 is closed and the capacitance diagram gauge CDG (133 Pa full scale) measures the differential pressure between the two volumes VR and VM. Afterwards, the valve V4 is opened to the flowmeter and the gas from the leak flows to the measurement volume VM, increasing the pressure inside it. The pressure variation is compensated by a volume decreasing carried out by a piston–bellows coupling described in [10]. The pressure variation is controlled between two thresholds by the reading of CDG: when the pressure inside VM exceeds the upper threshold, the piston–bellows coupling moves to perform a suitable volume variation DV to decrease the pressure to a value less than the lower threshold. The process is repeated more times, obtaining a saw-tooth variation of differential pressure between the two volumes in which each pressure decreasing corresponds to a movement of the piston–bellows coupling. The temperatures of VR and VM are measured and monitored by PT100 devices during each measurement. The molar gas flow q from the leak under calibration and can be expressed by the following approximated formula:
qffi
qpV patm DV M ¼ RT M Dt RT M
ð1Þ
where R is the universal gas constant, TM the temperature in the volume VM, DVM the volume variation carried out by the piston–bellows system, Dt is the time difference
a
between two points at the same pressure and qpV is the gas flow at temperature TM written in terms of throughput. The measurement procedure is automated and controlled by a software developed in labview ambient. Recently the flowmeter has been re-designed, changing the whole layout of the system to improve the compactness of the system and place the various components of the system in order to minimize thermal gradients, in particular between reference and measurement volumes VR and VM. An active thermal control has been introduced: the components of the system have been mounted on a aluminum board, realized with internal channels for the circulation of water, which temperature is controlled and maintained constant by an external water bath. The two pressure transducers (CDG and PG) have been placed inside apposite plexiglass chimneys to conduct outside the heat dissipated by the transducers. The whole flowmeter has been placed inside a plexiglass box to isolated it from external ambient. Fig. 2 shows the results of temperature stability obtained with and without active thermal control: the measurements, carried out by a set of PT100 sensors, show that the stability for a time of about 30 min is better than 0.005 °C, while the long term stability (about 20 h) has been improved of a 10-factor. In Fig. 3, the thermal drift measured with or without the active thermal control is shown: the temperature effect has been strongly reduced and its influence can be estimated by least squares method applied to the CDG pressure curve versus time obtained in the first 100 s of measurement in which the valve V3 is closed and the valve V4 is still open to the ambient and closed to the flowmeter. The maximum variation of temperature differences between reference and measurement volume during each measurement cycle has been 1.9 lK/s, correspondent to an effect which is less than 1% of the minimum gas flow rate measured by the flowmeter. 3. Measurement model and uncertainty budget The model adopted for the determination of molar gas flow delivered from a leak is a directly consequence of the application of the ideal gas law:
b
Fig. 1. (a) Scheme of primary standard flowmeter. VR and VM: reference and measurement volumes; TC1 and TC2: thermal control boxes respectively for the whole flowmeter and the leak under calibration; RTDs: temperature sensors; CDG: capacitance diaphragm gauge (133 Pa); PG: pressure gauge for reference atmospheric pressure measurement. (b): Saw-tooth variation of CDG differential pressure versus time.
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a
b
Fig. 2. Temperature stability for a time interval of 20 h; (a) passive thermal control; (b) active thermal control.
The global temperature effect on measurement is estimated measuring the pressure drift registered by CDG after the closing of valve V3 (volume VR and VM are separated), before introducing the gas inside the measurement volume. The drift is estimated by least squares method, obtaining the slope mc related to temperature influence, fitting the differential pressure from CDG versus time. As consequence of this, the measurand is given by the following equation, which represents the final model used for the calculation of gas flow and its standard uncertainty:
Fig. 3. CDG-pressure versus time after the closure of valve V3, before the entrance of gas from leak under calibration, with passive or active thermal control.
patm V M ¼ NRT M
ð2Þ
where N is the number of gas moles in VM at the initial time t0. Under the assumptions that the effects of adsorption and eventual leakage of molecules in VR and VM and the variation of the two volumes due to temperature are negligible, the molar gas flow at the time t1 = t0 + Dt, is given by:
q¼
DN patm DV M V M Dpatm p DT M ¼ þ V M atm Dt RT M Dt RT M Dt RT 2M Dt
ð3Þ
in which the first term in the right side is the quantity considered for the final determination of gas flow in a constant pressure–variable volume flowmeter, while the other terms are spurious terms which arise from reference pressure and temperature variations. For what concern the second term, as the valve V2 is closed before opening valve V4, the influence of atmospheric pressure variation (on the primary flowmeter) can be neglected: the changes versus time of the reference pressure practically depends only by thermal effect, so the Eq. (3) is re-written as:
q¼
patm DV M V M patm DT R p DT M þ V M atm RT M Dt RT M T R Dt RT 2M Dt
ð4Þ
Eq. (4) shows clearly again that the accuracy of the gas flow rate measurements strongly depends from the temperature stability of the system which has to be monitored.
q¼
1 h h X
"
2
1 d p p DLi RT M;i atm 4 i¼1 h 1X 1 DV M;i patm ¼ h i¼1 RT M;i Dt i
ni niþ1 mi mc miþ1 mc
#
ð5Þ where the index i is related to each pressure increase (Fig. 1), d is the piston diameter, DLi the displacement variation carried out to decrease the reading of CDG to a value less than the lower threshold, mi and ni respectively the slope and the intercept for each pressure rise, estimated by a least squares linear fit. Eq. (5) expresses the relationship between the measurand (the output quantity q) and the input quantities and it can be used to evaluate the standard uncertainty of gas flow q [12] starting from the standard uncertainty of each input quantity. The reference atmospheric pressure patm is measured by a MKS Baratron CDG (133 kPa full scale), which is periodically calibrated against INRIM interferometric mercury manometer. The uncertainty u(patm) is due to calibration uncertainty, resolution, repeatability of data acquisition during each measurement and stability of the gauge; u(patm) was evaluated as 80 Pa. The geometrical characterization of piston was performed at INRIM, after the choice of the optimal piston for the best piston–bellows coupling [10]. The standard uncertainty of its diameter u(d) is 5.0 106 m. The measurement of piston displacement is determined by a stepping-motor. The uncertainty u(DL) depends substantially on resolution and repeatability of stepping motor
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drive. It was recently characterized at INRIM by a Michelson interferometer mounted on the flowmeter and capable of working during the gas flow measurements. As results, standard uncertainty u(DL) = 1.2 106 m was obtained. The interferometric measurements were carried out for different steps of the motor and revealed a critical point related to the use of the flowmeter at low gas flow rate. For throughputs qpV < 5 106 Pa m3/s typical values of nominal displacement DL are between 30 lm and 100 lm with a relative standard uncertainty ranging from 4.0% to 1.2%. The parameters mc, mi and ni are estimated by linear regression of pressure versus time, applied in accordance of Gauss Markov theorem, taking into account the correlation between the couple mi and ni related to each pressure rise. The time measurements for linear regressions are performed by the PC internal clock, which is traceable to INRIM atomic clock; as the relative time accuracy is better than 5 105, the uncertainty component arisen from time measurement is negligible; the Gauss Markov theorem is applied under the hypothesis that the pressure measurements from CDG have the same variance and the variance of time is negligible, obtaining a linear estimate of the parameters with minimal variance and not polarized [13]. The uncertainties related to these parameters can be considered negligible as the relative standard uncertainty of time difference Dt = ni/(mi mc) – gi+1/(mi+1 mc) is less than 8 104. The temperature of the measurement volume of the flowmeter has been measured by a temperature sensor traced to ITS at INRIM. The standard uncertainty, due to calibration, repeatability and temperature gradients in VM is 0.1 K. The type A uncertainty of measurement has been evaluated with a standard uncertainty ranging from 8.8 1012 mol/s to 6.8 1010 mol/s in the working range of the flowmeter; type A uncertainty is evaluated following the correction suggested in [14] to take into account the limited number of repeated measurement. Table 1 shows the standard uncertainties of the input quantities of model Eq. (5) and type A uncertainty of gas flow rate measurement in the working range of the flowmeter. The combined relative standard uncertainties range from 4.6 102 to 0.4 102 between 4 1010 mol/s and 2 107 mol/s. The dominating contributions to the molar gas flow uncertainty are due to the piston displacement measurement, especially at lower gas flow, and to the type A uncertainty, which is not only due to the primary system but
Fig. 4. Temperature dependence of a stainless steel capillary for different gases between 15 °C and 30 °C.
depends also from stability of standard leak under calibration. 4. Temperature dependence of gas flow by capillary leaks with outlet to atmosphere The influence of temperature on the gas flow released by the leak devices has to be carefully considered [15], as it could considerably change the value of nominal gas flows generated by the leaks and provide inaccurate calibrations of leak detectors. A study of temperature dependence of stainless-steel capillary leak has been carried out with different gases, with the assumption of linear model in the considered range between 15 °C and 30 °C:
qT ¼ qT 0 ð1 þ aDTÞ;
DT ¼ ðT 20Þ C
ð6Þ
where qT is the gas flow measured at the temperature T, qT 0 the gas flow at the reference temperature of 20 °C and a is the temperature coefficient. The measurements have been performed with helium, nitrogen, argon and R134a, to include the most frequently used gases. Fig. 4 shows the results in term of throughput versus temperature difference DT. The temperature coefficients have been negative for all the considered gases. The results can be explained assuming the hypothesis of viscous regime, for which an increase of temperature causes an increase of viscosity, determining a decrease of the conductance of the capillary. The temperature coefficients have been estimated by least squares method, obtaining the following values:
Table 1 Standard uncertainties of the input quantities of model Eq. (5) and type A uncertainty of gas flow rate measurement in the range between 4 1010 mol/s to 2 107 mol/s. Input quantity xi
Distribution
Source of uncertainty
u(xi)
patm d DLi Tm,i Dti
Normal Normal Normal Normal
Calibration uncertainty, resolution, repeatability, stability Calibration uncertainty Calibration uncertainty, resolution, repeatability of stepping motor drive Calibration uncertainty, repeatability, temperature gradients Uncertainty of PC internal clock
80 Pa 5.0 106 m 1.2 106 m 0.1 K Negligible
Normal
Type A uncertainty of gas flow rate measurement
8.8 1012 mol/s–6.8 1010 mol/s
M. Bergoglio, D. Mari / Measurement 45 (2012) 2459–2463
aNitrogen ¼ ð0:00415 0:00004Þ C1 aArgon ¼ ð0:00398 0:00005Þ C1 aHelium ¼ ð0:00364 0:00004Þ C1 aR134a ¼ ð0:00429 0:0007Þ C1 The study verified that in most of cases concerning with useful applications of gas flow measurements with outlet to atmosphere, the gas flow released by a reference capillary leak is in viscous regime, so the gas flow ratio of two different gases is proportional to the inverse ratio of their viscosity. 5. Conclusions In the last years, at INRIM a new primary standard was designed and realized to measure molar gas flows with reference to atmospheric pressure. It is a constant pressure– variable volume flowmeter working with any tracer gas, between 4 1010 mol/s and 2 107 mol/s with a relative standard uncertainty ranging from 4.6 102 to 0.4 102. The combined standard uncertainty of molar gas flow is mainly due to the piston displacement measurement, especially at lower gas flow, and to the type A uncertainty. Recently the system has been modified in order to improve its accuracy; the whole layout of flowmeter has been changed and an active thermal control has been introduced, to get better the thermal contact between the various components of the system and minimized the temperature gradients in the flowmeter. In particular the variations of thermal gradients between reference and measurement volumes has been considered, as those variations produce disturbing effects on the real gas flow measured by the flowmeter. The active thermal control has strongly reduce the thermal drift occurred before the entrance of gas in the system and the maximum variation of thermal gradients between reference and measurement volumes has been equal to 1.9 lK/s, correspondent to an effect which is less than 1% of the minimum gas flow measured by the flowmeter.
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The temperature dependence of the gas flow released by a capillary leak has been studied in the range between 15 °C and 30 °C with different gases (N2, Ar, He, R134a). The results have shown that the temperature coefficient is negative confirming that in most of cases the gas flows with outlet to atmospheric pressure are in viscous regime. The experimental value of temperature coefficient has been less than 0.005 °C1 for all the considered gases. References [1] A. Calcatelli, M. Bergoglio, D. Mari, Leak detection, calibrations and reference flows: practical example, Vacuum 81 (11–12) (2007) 1538–1544. [2] K.E. McCulloh, C.R. Tilford, C.D. Ehrlich, F.G. Long, Low-range flowmeters for use with vacuum and leak standards, J. Vac. Sci. Technol. A 5 (1987) 376–381. [3] W. Jitschin, U. Weber, H.K. Hartmann, Convenient gas primary flow meter, Vacuum 46 (8) (1995) 821–824. [4] K. Jousten, H. Menzer, R. Niepraschk, A new fully automated gas flowmeter at the PTB for flow rates between 1013 mol/s and 106 mol/s, Metrologia 39 (2002) 519–529. [5] A. Calcatelli, G. Raiteri, G. Rumiano, The IMGC-CNR flowmeter for automatic measurements of low-range gas flows, Measurement 34 (2) (2003) 121–132. [6] T. Gronych, L. Peksa, P. Repa, J. Wild, J. Tesar, D. Prazak, Z. Krajicek, M. Vicar, The use of diaphragm bellows to construct a constant pressure gas flowmeter for the flow rate range 107–101 Pa m3 s1 to 101 Pa m3 s1, Metrologia 45 (1) (2008) 46–52. [7] K. Jousten, H. Menzer, D. Wandrey, R. Niepraschk, New, fully automated, primary standard for generating vacuum pressures between 1010 Pa and 3 102 Pa with respect to residual pressure, Metrologia 36 (1999) 493–497. [8] M. Bergoglio, D. Mari, INRIM continuous expansion system as high vacuum primary standard for gas pressure measurements below 9 102 Pa, Vacuum 84 (1) (2009) 270–273. [9] K. Jousten, U. Becker, A primary standard for the calibration of sniffer test leak devices, Metrologia 46 (2009) 560–568. [10] F. Alasia, A. Calcatelli, G. Cignolo, G. Raiteri, G. Rumiano, in: IMEKO TC 16 International Symposium on Pressure and Vacuum, Proceedings of Acta Metrologica Sinica Press, 2003. [11] I. Morgado, J.C. Legras, D. Clodic, Primary standard for the calibration of refrigerant leak flow rates, Metrologia 47 (2010) 135–145. [12] BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML 2008, Evaluation of Measurement Data-Guide to the Expression of Uncertainty in Measurement, JCGM 100 (accessed 16.11.09). [13] G. Mana, Data analysis and optimum estimate, Lect. Notes Turin Polytech. (2001). [14] R. Kacker, A. Jones, On use of bayesian statistics to make the guide to the expression of uncertainty in measurement consistent, Metrologia 40 (2003) 235–248. [15] W. W Große Bley, Temperature dependence and long term behaviour of capillary-type helium reference leaks with gas reservoir, Vacuum 41 (7–9) (1990) 1863–1865.
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
INRIM primary standard for microgas-flow measurements with reference to atmospheric pressure Mercede Bergoglio, Domenico Mari ⇑ Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy
a r t i c l e
i n f o
Article history: Available online 15 November 2011 Keywords: Gas flow Primary standard Reference leak
a b s t r a c t Primary standard flowmeters are developed for the calibration of leak devices used in many applications in which is necessary to detect and quantify gas leakage from a material, a component or a system. At INRIM, a primary standard was designed and realized for the measurement of molar gas flow from 4 1010 mol/s to 2 107 mol/s with reference to atmospheric pressure. It is based on the constant-pressure–variable-volume method and is able to work with any tracer gas. The paper describes the primary standard, the mathematical model adopted for the estimate of the measurand and the uncertainty evaluation. The recent developments of the system, performed to improve the accuracy of the standard, are presented. The new layout of the flowmeter has allowed a study of the temperature effects on the gas flow measurements in the range between 15 °C and 30 °C. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Leak detection techniques [1] are applied in many fields of science and technology to verify if an object under control satisfies the required limits by a scientific study or prescribed specifications. Leak detectors are instruments for leak testing of materials, components, systems and they are periodically calibrated by leak devices, which are widely used secondary standards of gas flow. Primary standard micro-gas flowmeters have been developed to ensure traceability for gas flow measurements and provide system capable to generate and measure primary standard gas flows for the calibration of leak devices [2–6] or to be used in conjunction with continuous expansion systems [7,8]. In the last years many applications and instruments, in which leak testing is carried out with reference to atmospheric pressure, have been developed. Recently, National Metrological Institutes have realized primary standards [9–11] for the gas flow measurements with outlet to atmospheric pressure in order to provide the necessary support ⇑ Corresponding author. E-mail address: [email protected] (D. Mari). 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.10.039
for a correct traceability chain in this new flow metrology field, related to micro-gas flowing to the atmosphere. The paper describes the primary standard flowmeter designed, realized and recently improved at INRIM for the measurement of molar gas flow with reference to atmospheric pressure. It is based on the constant-pressure–variable-volume method and is able to work with any tracer gas, between 4 1010 mol/s and 2 107 mol/s with a relative standard uncertainty ranging from 4.6 102 to 0.4 102. In the last part of the paper, the temperature dependence of gas flow delivered by a capillary leak, calibrated by the primary standard flowmeter, is studied in the range between 15 °C and 30 °C. The results provide an experimental determination of the capillary thermal coefficient for different gases to take into account the influence of temperature when the measurements are performed with reference to atmosphere. 2. Description of the system and measurement procedure The quantity generated by a leak device and measured by a primary standard is the molar gas flow, which can
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be defined as the number of gas moles coming out from the leak per unit time. The INRIM primary standard flowmeter is based on constant-pressure and variable-volume method and it can measure molar flow rate in the range between from 4 1010 mol/s to 2 107 mol/s with reference to atmospheric pressure. Fig. 1 shows the scheme of the system: at the beginning of operation the reference and measurement volumes VR and VM are maintained at the same atmospheric reference pressure patm with valves V1, V2 and V3 opened and the three-way valve closed to the system and opened to air, in order to channel the gas flowing out from the device towards the air and avoid a strong accumulation of gas inside the leak. After the closing of valve V2, to eliminate eventual influence of reference pressure variations in VR, the valve V3 is closed and the capacitance diagram gauge CDG (133 Pa full scale) measures the differential pressure between the two volumes VR and VM. Afterwards, the valve V4 is opened to the flowmeter and the gas from the leak flows to the measurement volume VM, increasing the pressure inside it. The pressure variation is compensated by a volume decreasing carried out by a piston–bellows coupling described in [10]. The pressure variation is controlled between two thresholds by the reading of CDG: when the pressure inside VM exceeds the upper threshold, the piston–bellows coupling moves to perform a suitable volume variation DV to decrease the pressure to a value less than the lower threshold. The process is repeated more times, obtaining a saw-tooth variation of differential pressure between the two volumes in which each pressure decreasing corresponds to a movement of the piston–bellows coupling. The temperatures of VR and VM are measured and monitored by PT100 devices during each measurement. The molar gas flow q from the leak under calibration and can be expressed by the following approximated formula:
qffi
qpV patm DV M ¼ RT M Dt RT M
ð1Þ
where R is the universal gas constant, TM the temperature in the volume VM, DVM the volume variation carried out by the piston–bellows system, Dt is the time difference
a
between two points at the same pressure and qpV is the gas flow at temperature TM written in terms of throughput. The measurement procedure is automated and controlled by a software developed in labview ambient. Recently the flowmeter has been re-designed, changing the whole layout of the system to improve the compactness of the system and place the various components of the system in order to minimize thermal gradients, in particular between reference and measurement volumes VR and VM. An active thermal control has been introduced: the components of the system have been mounted on a aluminum board, realized with internal channels for the circulation of water, which temperature is controlled and maintained constant by an external water bath. The two pressure transducers (CDG and PG) have been placed inside apposite plexiglass chimneys to conduct outside the heat dissipated by the transducers. The whole flowmeter has been placed inside a plexiglass box to isolated it from external ambient. Fig. 2 shows the results of temperature stability obtained with and without active thermal control: the measurements, carried out by a set of PT100 sensors, show that the stability for a time of about 30 min is better than 0.005 °C, while the long term stability (about 20 h) has been improved of a 10-factor. In Fig. 3, the thermal drift measured with or without the active thermal control is shown: the temperature effect has been strongly reduced and its influence can be estimated by least squares method applied to the CDG pressure curve versus time obtained in the first 100 s of measurement in which the valve V3 is closed and the valve V4 is still open to the ambient and closed to the flowmeter. The maximum variation of temperature differences between reference and measurement volume during each measurement cycle has been 1.9 lK/s, correspondent to an effect which is less than 1% of the minimum gas flow rate measured by the flowmeter. 3. Measurement model and uncertainty budget The model adopted for the determination of molar gas flow delivered from a leak is a directly consequence of the application of the ideal gas law:
b
Fig. 1. (a) Scheme of primary standard flowmeter. VR and VM: reference and measurement volumes; TC1 and TC2: thermal control boxes respectively for the whole flowmeter and the leak under calibration; RTDs: temperature sensors; CDG: capacitance diaphragm gauge (133 Pa); PG: pressure gauge for reference atmospheric pressure measurement. (b): Saw-tooth variation of CDG differential pressure versus time.
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a
b
Fig. 2. Temperature stability for a time interval of 20 h; (a) passive thermal control; (b) active thermal control.
The global temperature effect on measurement is estimated measuring the pressure drift registered by CDG after the closing of valve V3 (volume VR and VM are separated), before introducing the gas inside the measurement volume. The drift is estimated by least squares method, obtaining the slope mc related to temperature influence, fitting the differential pressure from CDG versus time. As consequence of this, the measurand is given by the following equation, which represents the final model used for the calculation of gas flow and its standard uncertainty:
Fig. 3. CDG-pressure versus time after the closure of valve V3, before the entrance of gas from leak under calibration, with passive or active thermal control.
patm V M ¼ NRT M
ð2Þ
where N is the number of gas moles in VM at the initial time t0. Under the assumptions that the effects of adsorption and eventual leakage of molecules in VR and VM and the variation of the two volumes due to temperature are negligible, the molar gas flow at the time t1 = t0 + Dt, is given by:
q¼
DN patm DV M V M Dpatm p DT M ¼ þ V M atm Dt RT M Dt RT M Dt RT 2M Dt
ð3Þ
in which the first term in the right side is the quantity considered for the final determination of gas flow in a constant pressure–variable volume flowmeter, while the other terms are spurious terms which arise from reference pressure and temperature variations. For what concern the second term, as the valve V2 is closed before opening valve V4, the influence of atmospheric pressure variation (on the primary flowmeter) can be neglected: the changes versus time of the reference pressure practically depends only by thermal effect, so the Eq. (3) is re-written as:
q¼
patm DV M V M patm DT R p DT M þ V M atm RT M Dt RT M T R Dt RT 2M Dt
ð4Þ
Eq. (4) shows clearly again that the accuracy of the gas flow rate measurements strongly depends from the temperature stability of the system which has to be monitored.
q¼
1 h h X
"
2
1 d p p DLi RT M;i atm 4 i¼1 h 1X 1 DV M;i patm ¼ h i¼1 RT M;i Dt i
ni niþ1 mi mc miþ1 mc
#
ð5Þ where the index i is related to each pressure increase (Fig. 1), d is the piston diameter, DLi the displacement variation carried out to decrease the reading of CDG to a value less than the lower threshold, mi and ni respectively the slope and the intercept for each pressure rise, estimated by a least squares linear fit. Eq. (5) expresses the relationship between the measurand (the output quantity q) and the input quantities and it can be used to evaluate the standard uncertainty of gas flow q [12] starting from the standard uncertainty of each input quantity. The reference atmospheric pressure patm is measured by a MKS Baratron CDG (133 kPa full scale), which is periodically calibrated against INRIM interferometric mercury manometer. The uncertainty u(patm) is due to calibration uncertainty, resolution, repeatability of data acquisition during each measurement and stability of the gauge; u(patm) was evaluated as 80 Pa. The geometrical characterization of piston was performed at INRIM, after the choice of the optimal piston for the best piston–bellows coupling [10]. The standard uncertainty of its diameter u(d) is 5.0 106 m. The measurement of piston displacement is determined by a stepping-motor. The uncertainty u(DL) depends substantially on resolution and repeatability of stepping motor
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drive. It was recently characterized at INRIM by a Michelson interferometer mounted on the flowmeter and capable of working during the gas flow measurements. As results, standard uncertainty u(DL) = 1.2 106 m was obtained. The interferometric measurements were carried out for different steps of the motor and revealed a critical point related to the use of the flowmeter at low gas flow rate. For throughputs qpV < 5 106 Pa m3/s typical values of nominal displacement DL are between 30 lm and 100 lm with a relative standard uncertainty ranging from 4.0% to 1.2%. The parameters mc, mi and ni are estimated by linear regression of pressure versus time, applied in accordance of Gauss Markov theorem, taking into account the correlation between the couple mi and ni related to each pressure rise. The time measurements for linear regressions are performed by the PC internal clock, which is traceable to INRIM atomic clock; as the relative time accuracy is better than 5 105, the uncertainty component arisen from time measurement is negligible; the Gauss Markov theorem is applied under the hypothesis that the pressure measurements from CDG have the same variance and the variance of time is negligible, obtaining a linear estimate of the parameters with minimal variance and not polarized [13]. The uncertainties related to these parameters can be considered negligible as the relative standard uncertainty of time difference Dt = ni/(mi mc) – gi+1/(mi+1 mc) is less than 8 104. The temperature of the measurement volume of the flowmeter has been measured by a temperature sensor traced to ITS at INRIM. The standard uncertainty, due to calibration, repeatability and temperature gradients in VM is 0.1 K. The type A uncertainty of measurement has been evaluated with a standard uncertainty ranging from 8.8 1012 mol/s to 6.8 1010 mol/s in the working range of the flowmeter; type A uncertainty is evaluated following the correction suggested in [14] to take into account the limited number of repeated measurement. Table 1 shows the standard uncertainties of the input quantities of model Eq. (5) and type A uncertainty of gas flow rate measurement in the working range of the flowmeter. The combined relative standard uncertainties range from 4.6 102 to 0.4 102 between 4 1010 mol/s and 2 107 mol/s. The dominating contributions to the molar gas flow uncertainty are due to the piston displacement measurement, especially at lower gas flow, and to the type A uncertainty, which is not only due to the primary system but
Fig. 4. Temperature dependence of a stainless steel capillary for different gases between 15 °C and 30 °C.
depends also from stability of standard leak under calibration. 4. Temperature dependence of gas flow by capillary leaks with outlet to atmosphere The influence of temperature on the gas flow released by the leak devices has to be carefully considered [15], as it could considerably change the value of nominal gas flows generated by the leaks and provide inaccurate calibrations of leak detectors. A study of temperature dependence of stainless-steel capillary leak has been carried out with different gases, with the assumption of linear model in the considered range between 15 °C and 30 °C:
qT ¼ qT 0 ð1 þ aDTÞ;
DT ¼ ðT 20Þ C
ð6Þ
where qT is the gas flow measured at the temperature T, qT 0 the gas flow at the reference temperature of 20 °C and a is the temperature coefficient. The measurements have been performed with helium, nitrogen, argon and R134a, to include the most frequently used gases. Fig. 4 shows the results in term of throughput versus temperature difference DT. The temperature coefficients have been negative for all the considered gases. The results can be explained assuming the hypothesis of viscous regime, for which an increase of temperature causes an increase of viscosity, determining a decrease of the conductance of the capillary. The temperature coefficients have been estimated by least squares method, obtaining the following values:
Table 1 Standard uncertainties of the input quantities of model Eq. (5) and type A uncertainty of gas flow rate measurement in the range between 4 1010 mol/s to 2 107 mol/s. Input quantity xi
Distribution
Source of uncertainty
u(xi)
patm d DLi Tm,i Dti
Normal Normal Normal Normal
Calibration uncertainty, resolution, repeatability, stability Calibration uncertainty Calibration uncertainty, resolution, repeatability of stepping motor drive Calibration uncertainty, repeatability, temperature gradients Uncertainty of PC internal clock
80 Pa 5.0 106 m 1.2 106 m 0.1 K Negligible
Normal
Type A uncertainty of gas flow rate measurement
8.8 1012 mol/s–6.8 1010 mol/s
M. Bergoglio, D. Mari / Measurement 45 (2012) 2459–2463
aNitrogen ¼ ð0:00415 0:00004Þ C1 aArgon ¼ ð0:00398 0:00005Þ C1 aHelium ¼ ð0:00364 0:00004Þ C1 aR134a ¼ ð0:00429 0:0007Þ C1 The study verified that in most of cases concerning with useful applications of gas flow measurements with outlet to atmosphere, the gas flow released by a reference capillary leak is in viscous regime, so the gas flow ratio of two different gases is proportional to the inverse ratio of their viscosity. 5. Conclusions In the last years, at INRIM a new primary standard was designed and realized to measure molar gas flows with reference to atmospheric pressure. It is a constant pressure– variable volume flowmeter working with any tracer gas, between 4 1010 mol/s and 2 107 mol/s with a relative standard uncertainty ranging from 4.6 102 to 0.4 102. The combined standard uncertainty of molar gas flow is mainly due to the piston displacement measurement, especially at lower gas flow, and to the type A uncertainty. Recently the system has been modified in order to improve its accuracy; the whole layout of flowmeter has been changed and an active thermal control has been introduced, to get better the thermal contact between the various components of the system and minimized the temperature gradients in the flowmeter. In particular the variations of thermal gradients between reference and measurement volumes has been considered, as those variations produce disturbing effects on the real gas flow measured by the flowmeter. The active thermal control has strongly reduce the thermal drift occurred before the entrance of gas in the system and the maximum variation of thermal gradients between reference and measurement volumes has been equal to 1.9 lK/s, correspondent to an effect which is less than 1% of the minimum gas flow measured by the flowmeter.
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The temperature dependence of the gas flow released by a capillary leak has been studied in the range between 15 °C and 30 °C with different gases (N2, Ar, He, R134a). The results have shown that the temperature coefficient is negative confirming that in most of cases the gas flows with outlet to atmospheric pressure are in viscous regime. The experimental value of temperature coefficient has been less than 0.005 °C1 for all the considered gases. References [1] A. Calcatelli, M. Bergoglio, D. Mari, Leak detection, calibrations and reference flows: practical example, Vacuum 81 (11–12) (2007) 1538–1544. [2] K.E. McCulloh, C.R. Tilford, C.D. Ehrlich, F.G. Long, Low-range flowmeters for use with vacuum and leak standards, J. Vac. Sci. Technol. A 5 (1987) 376–381. [3] W. Jitschin, U. Weber, H.K. Hartmann, Convenient gas primary flow meter, Vacuum 46 (8) (1995) 821–824. [4] K. Jousten, H. Menzer, R. Niepraschk, A new fully automated gas flowmeter at the PTB for flow rates between 1013 mol/s and 106 mol/s, Metrologia 39 (2002) 519–529. [5] A. Calcatelli, G. Raiteri, G. Rumiano, The IMGC-CNR flowmeter for automatic measurements of low-range gas flows, Measurement 34 (2) (2003) 121–132. [6] T. Gronych, L. Peksa, P. Repa, J. Wild, J. Tesar, D. Prazak, Z. Krajicek, M. Vicar, The use of diaphragm bellows to construct a constant pressure gas flowmeter for the flow rate range 107–101 Pa m3 s1 to 101 Pa m3 s1, Metrologia 45 (1) (2008) 46–52. [7] K. Jousten, H. Menzer, D. Wandrey, R. Niepraschk, New, fully automated, primary standard for generating vacuum pressures between 1010 Pa and 3 102 Pa with respect to residual pressure, Metrologia 36 (1999) 493–497. [8] M. Bergoglio, D. Mari, INRIM continuous expansion system as high vacuum primary standard for gas pressure measurements below 9 102 Pa, Vacuum 84 (1) (2009) 270–273. [9] K. Jousten, U. Becker, A primary standard for the calibration of sniffer test leak devices, Metrologia 46 (2009) 560–568. [10] F. Alasia, A. Calcatelli, G. Cignolo, G. Raiteri, G. Rumiano, in: IMEKO TC 16 International Symposium on Pressure and Vacuum, Proceedings of Acta Metrologica Sinica Press, 2003. [11] I. Morgado, J.C. Legras, D. Clodic, Primary standard for the calibration of refrigerant leak flow rates, Metrologia 47 (2010) 135–145. [12] BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML 2008, Evaluation of Measurement Data-Guide to the Expression of Uncertainty in Measurement, JCGM 100 (accessed 16.11.09). [13] G. Mana, Data analysis and optimum estimate, Lect. Notes Turin Polytech. (2001). [14] R. Kacker, A. Jones, On use of bayesian statistics to make the guide to the expression of uncertainty in measurement consistent, Metrologia 40 (2003) 235–248. [15] W. W Große Bley, Temperature dependence and long term behaviour of capillary-type helium reference leaks with gas reservoir, Vacuum 41 (7–9) (1990) 1863–1865.