Determination and use of vibrometer mass flow error correction relationships.

Abstract

A method for determining a mass flow error correction relationship is provided. The method includes comparing each of a plurality of mass flow measurement values ​​of an alternate gas flow to a corresponding plurality of reference mass flow measurement values ​​of the alternate gas flow. The method also includes determining a plurality of mass flow measurement errors corresponding to a plurality of fluid velocity-related parameter values ​​of the alternate gas flow based on the comparison.

Description

[Technical Field]

[0001] The embodiments described below relate to correcting the mass flow rate of a vibrometer, and more particularly to determining and using a vibrometer mass flow rate error correction relationship. [Background technology]

[0002] Vibrometers, such as Coriolis mass flow meters, liquid densitometers, gas densitometers, liquid viscometers, gas / liquid specific gravity meters, gas / liquid relative density meters, and gas molecular weight meters, are commonly known and are used to measure fluid properties. Generally, a vibrometer comprises a sensor assembly and meter electronics. The material in or around the sensor assembly may be flowing or stationary. The vibrometer can be used to measure the mass flow rate, density, or other properties of the material in the sensor assembly.

[0003] For example, a Coriolis flow meter can measure mass flow. As an example, a Coriolis flow meter can provide a drive signal to a driver positioned between two parallel, balanced conduits containing a flowing fluid. The driver induces out-of-phase vibrations between the two conduits. Fluid flowing through the two conduits induces a phase difference between the inlets and outlets of the two conduits. This phase difference is measured by two pickoff sensors positioned on either side of the midpoint of the two conduits. For example, one pickoff may be proximate the inlets of the two conduits and another of the two pickoffs may be proximate the outlets of the two conduits. The measured phase difference is scaled by a flow calibration factor to obtain a mass flow measurement. When a gas is measured, the mass flow measurement typically includes an error, referred to as a mass flow measurement error, that correlates with the mass flow rate of the gas.

[0004] Therefore, calibration of a Coriolis flowmeter intended to measure gas flow typically involves determining the mass flow measurement error on a mass flow rate basis. For example, a reference Coriolis flowmeter connected in series with the Coriolis flowmeter being calibrated can provide a known mass flow measurement of the gas flow. The known mass flow measurement of the gas flow can be compared to an uncorrected mass flow measurement provided by the calibration target Coriolis flowmeter to determine the mass flow measurement error. This comparison to determine the mass flow measurement error can be performed at various mass flow rates of the gas flow to obtain pairs (e.g., ordered pairs) of mass flow measurement error values ​​and mass flow value values. The pairs can be used to correct subsequent uncorrected mass flow measurements obtained by the Coriolis flowmeter.

[0005] As can be appreciated, process gases may not be available for calibrating Coriolis flow meters. Therefore, alternative gases have been used to calibrate Coriolis flow meters. Alternative gases typically have densities that are different from the density of the process gas. This density difference can cause deviations in mass flow measurement error between different gases at a given flow rate. To reduce the effect of density on mass flow measurement error, the pressure of the alternative gas is adjusted so that its density is approximately the same as the density of the process gas for which the mass flow measurement is being corrected.

[0006] However, properties other than density can cause deviations between the mass flow measurement errors of the alternate gas flow and the process gas flow. As a result, if the deviation is large enough, the mass flow measurement error of the alternate gas flow cannot necessarily be used to correct the mass flow measurement error of the process gas flow. Therefore, there is a need to determine and use a mass flow error correction relationship for a vibrometer. Summary of the Invention

[0007] A method for determining a vibrometer mass flow error correction value is provided, according to one embodiment, the method includes comparing each of a plurality of mass flow measurement values ​​of an alternative gas flow to a corresponding plurality of reference mass flow measurement values ​​of the alternative gas flow, and determining a plurality of mass flow measurement errors corresponding to a plurality of fluid velocity-related parameter values ​​of the alternative gas flow based on the comparison.

[0008] A system for determining a mass flow error correction relationship for a vibrometer is provided, according to one embodiment, the system includes a vibrometer configured to measure the mass flow rate of an alternative gas flow, a reference device disposed in series with the vibrometer and configured to determine a reference mass flow rate of the alternative gas flow, and a calibration circuit in communication with the vibrometer and the reference device, the calibration circuit configured to perform the aforementioned method.

[0009] A method for using a vibrometer mass flow error correction relationship is provided, according to one embodiment, the method includes determining a fluid velocity-related parameter value for the process gas flow based on a measured mass flow value, a density value, and a cross-sectional area of ​​the process gas flow, and determining a mass flow error correction value based on the fluid velocity-related parameter value.

[0010] Meter electronics for using the mass flow error correction relationship is provided, according to one embodiment, comprising a storage system and a processing system communicatively coupled to the storage system, the processing system configured to perform the aforementioned method.

[0011] A vibrometer for using a mass flow error correction relationship is provided. According to one embodiment, the vibrometer comprises a sensor assembly configured to measure the mass flow rate of a process gas flow, and meter electronics communicatively connected to the sensor assembly, the meter electronics being as provided above.

[0012] [Aspect] According to one aspect, a method for determining a vibrometer mass flow error correction value includes comparing each of a plurality of mass flow measurements of an alternate gas flow to a corresponding plurality of reference mass flow measurements of the alternate gas flow, and determining a plurality of mass flow measurement errors corresponding to a plurality of fluid velocity-related parameter values ​​of the alternate gas flow based on the comparison.

[0013] Preferably, the plurality of fluid velocity related parameter values ​​of the alternative gas flow include one of a plurality of fluid velocity values ​​and a plurality of Mach number values ​​of the alternative gas flow.

[0014] Preferably, the plurality of reference mass flow measurements of the alternative gas stream are provided by a reference device disposed in series with the vibrometer.

[0015] Preferably, the alternative gas stream comprises one of air, natural gas, carbon dioxide, nitrogen, and helium.

[0016] Preferably, the plurality of mass flow measurement errors corresponding to the plurality of fluid velocity-related parameter values ​​of the alternative gas flow include a plurality of differences between each of the plurality of mass flow measurement values ​​and a corresponding each of the plurality of reference mass flow measurement values.

[0017] Preferably, the method further comprises the step of flowing said alternative gas flow through said vibrometer.

[0018] Preferably, the method further comprises the step of determining, using the vibrometer, the plurality of mass flow rate measurements at a corresponding plurality of fluid velocity related parameter values ​​of the alternative gas flow.

[0019] Preferably, the method further comprises storing the plurality of mass flow measurement errors in meter electronics of the vibrometer as a plurality of ordered pairs of the plurality of mass flow measurement errors and a corresponding plurality of said fluid velocity-related parameter values.

[0020] Preferably, the method further includes determining a mass flow error correction relationship based on the plurality of mass flow measurement errors and the corresponding plurality of fluid velocity-related parameter values, and storing the mass flow error correction relationship in the vibrometer.

[0021] According to one aspect, a system for determining a mass flow error correction relationship for a vibrometer includes a vibrometer configured to measure a mass flow rate of an alternative gas flow, a reference device disposed in series with the vibrometer and configured to determine a reference mass flow rate of the alternative gas flow, and a calibration circuit in communication with the vibrometer and the reference device, the calibration circuit configured to perform the aforementioned method.

[0022] According to one aspect, a method for using a vibrometer mass flow error correction relationship includes determining a fluid velocity-related parameter value of a process gas flow based on measured mass flow values, density values, and cross-sectional area of ​​the process gas flow, and determining a mass flow error correction value based on the fluid velocity-related parameter value.

[0023] Preferably, the fluid velocity related parameter value comprises one of a fluid velocity value and a Mach number value of the process gas flow.

[0024] Preferably, the process gas stream is a hydrogen gas stream.

[0025] Preferably, the method further comprises measuring the mass flow rate of the process gas flow using the vibrometer and determining a measured mass flow rate value.

[0026] Preferably, the method further comprises the step of correcting the measured mass flow value with the mass flow error correction value.

[0027] Preferably, the step of determining a mass flow error correction value based on the fluid velocity related parameter value includes obtaining a mass flow error correction relationship for an alternative gas flow, and determining a mass flow correction value based on the mass flow error correction relationship for said alternative gas flow and said fluid velocity related parameter value.

[0028] Preferably, the alternative gas stream comprises one of air, natural gas, carbon dioxide, nitrogen, and helium.

[0029] According to one aspect, meter electronics for using a mass flow error correction relationship includes a storage system and a processing system communicatively coupled to the storage system, the processing system configured to perform the aforementioned method.

[0030] According to one aspect, a vibrometer using a mass flow error correction relationship includes a sensor assembly configured to measure the mass flow rate of a process gas flow, and meter electronics communicatively connected to the sensor assembly, the meter electronics being provided as described above. [Brief explanation of the drawings]

[0031] Like reference numbers represent like elements in all drawings. It should be understood that the drawings are not necessarily to scale. [Figure 1] FIG. 1 illustrates a vibrometer 5 configured to determine and use a mass flow error correction relationship for the vibrometer 5 . [Figure 2] FIG. 2 shows a block diagram of a vibrometer 5, including a block diagram of meter electronics 20 configured to determine and use the vibrometer 5 mass flow error correction value. [Figure 3] FIG. 3 shows meter electronics 20 for determining and using the mass flow error compensation relationship of vibrometer 5. [Figure 4] FIG. 4 shows a graph 400 illustrating the lack of a discernible relationship between the percentage of mass flow error and mass flow rate. [Figure 5]FIG. 5 shows a graph 500 illustrating a discernible relationship between the percentage of mass flow error and a fluid velocity related parameter. [Figure 6] FIG. 6 shows a graph 600 illustrating a discernible relationship between the percentage of mass flow error and a fluid velocity related parameter. [Figure 7] FIG. 7 shows a graph 700 illustrating the lack of a discernible relationship between the percentage of mass flow error and mass flow rate. [Figure 8] FIG. 8 shows a graph 800 illustrating a discernible relationship between the percentage of mass flow error and a fluid velocity related parameter. [Figure 9] FIG. 9 shows a graph 900 illustrating a discernible relationship between the mass flow error percentage and the fluid velocity related parameter after the mass flow error correction relationship has been applied. [Figure 10] FIG. 10 illustrates a system 1000 for determining a vibrometer mass flow error correction relationship. [Figure 11] FIG. 11 illustrates a method 1100 for determining a mass flow error correction relationship for a vibrometer, such as vibrometer 5 described above. [Figure 12] FIG. 12 illustrates a method 1200 for using the mass flow error correction relationship of a vibrometer, such as vibrometer 5 described above. DETAILED DESCRIPTION OF THE INVENTION

[0032] 1-12 and the following description provide specific examples to teach those skilled in the art how to make and use the best modes of embodiments relating to determining and using a vibrometer mass flow error correction relationship. Some conventional aspects have been simplified or omitted for the purpose of teaching the principles of the invention. Those skilled in the art will appreciate variations of these examples that fall within the scope of the present disclosure. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of determining and using a vibrometer mass flow error correction relationship. Therefore, the embodiments described below are not limited to the specific examples described below, but only by the claims and their equivalents.

[0033] FIGURE 1 illustrates a vibrometer 5 configured to determine and use a mass flow error correction relationship for the vibrometer 5. As shown in FIGURE 1, the vibrometer 5 is a Coriolis flow meter that includes a sensor assembly 10 and meter electronics 20. The sensor assembly 10 responds to the mass flow rate and density of a process material. The meter electronics 20 is connected to the sensor assembly 10 via leads 100 and provides density, mass flow rate, and temperature information, as well as other information, via port 26.

[0034] The sensor assembly 10 includes a pair of manifolds 150 and 150′, flanges 103 and 103′ having flange necks 110 and 110′, a pair of parallel conduits 130 and 130′, a driver 180, a resistance temperature detector (RTD) 190, and a pair of pickoff sensors 170l and 170r. The conduits 130 and 130′ have two substantially straight inlet legs 131 and 131′ and outlet legs 134 and 134′ that converge toward each other at the conduit mounting blocks 120 and 120′. The conduits 130 and 130′ bend at two symmetrical locations along their lengths and are substantially parallel throughout their entire lengths. Brace bars 140 and 140′ serve to define axes W and W′ about which each conduit 130 and 130′ oscillates. Legs 131, 131′ and 134, 134′ of conduits 130, 130′ are fixedly attached to conduit mounting blocks 120 and 120′, which are in turn fixedly attached to manifolds 150 and 150′. This provides a continuous, closed material path through sensor assembly 10.

[0035] When flanges 103 and 103', having holes 102 and 102', are connected via inlet end 104 and outlet end 104' to a process line (not shown) carrying the process material being measured, the material enters the vibrometer at inlet end 104 through orifice 101 in flange 103 and is directed through manifold 150 to conduit mounting block 120, having surface 121. Within manifold 150, the material is split and directed through conduits 130, 130'. Upon exiting conduits 130, 130', the process material recombines in block 120', having surface 121', and manifold 150' into a single stream before being directed to outlet end 104', which is connected to the process line (not shown) by flange 103', having hole 102'.

[0036] The conduits 130, 130' are selected to have substantially the same mass distribution, moment of inertia, and Young's modulus about bending axes W-W and W'-W', respectively, and are appropriately mounted to the conduit mounting blocks 120, 120'. These bending axes pass through the brace bars 140, 140'. Because the Young's modulus of the conduit changes with temperature, which affects flow rate and density calculations, an RTD 190 is attached to the conduit 130' to continuously measure the temperature of the conduit 130'. The temperature of the conduit 130', and therefore the voltage appearing across it for a given current passing through the RTD 190, depends on the temperature of the material passing through the conduit 130'. The temperature-dependent voltage appearing across the RTD 190 is used by the meter electronics 20 in a well-known manner to compensate for changes in the elastic modulus of the conduits 130, 130' due to changes in the conduit temperature. The RTD 190 is connected to the meter electronics 20 by leads 195.

[0037] Both conduits 130, 130' are driven in opposite directions about their respective bending axes W and W' in what is referred to as the first out-of-phase bending mode of the vibrometer by a driver 180. This driver 180 may comprise any one of a number of well-known configurations, such as a magnet attached to conduit 130' and an opposing coil attached to conduit 130 through which an alternating current is passed to vibrate both conduits 130, 130'. An appropriate drive signal 185 is supplied to driver 180 by meter electronics 20 via leads.

[0038] Meter electronics 20 receives the RTD temperature signal on lead 190 and sensor signal 165 appearing on lead 100, which carries left and right sensor signals 165l and 165r, respectively. Meter electronics 20 generates drive signal 185 appearing on lead to driver 180, causing conduits 130 and 130' to vibrate. Meter electronics 20 processes left and right sensor signals 165l and 165r and RTD signal 190 to calculate the mass flow rate and density of material passing through sensor assembly 10. This information, along with other information, is applied by meter electronics 20 as signals via path 26. A more detailed discussion of meter electronics 20 is provided below.

[0039] 2 shows a block diagram of vibrometer 5, including a block diagram of meter electronics 20 configured to determine and use a mass flow error correction value for vibrometer 5. As shown in FIG. 2, meter electronics 20 is communicatively coupled to sensor assembly 10. As previously described with reference to FIG. 1, sensor assembly 10 includes left and right pickoff sensors 170l, 170r, driver 180, and temperature sensor 190, which are communicatively coupled to meter electronics 20 through set of leads 100 via communication channel 112.

[0040] Meter electronics 20 provides drive signals 185 via leads 100. More specifically, meter electronics 20 provides drive signals 185 to drivers 180 within sensor assembly 10. Additionally, sensor signals 165, including left sensor signal 165l and right sensor signal 165r, are provided by sensor assembly 10. More specifically, in the illustrated embodiment, sensor signals 165 are provided by left and right pickoff sensors 170l, 170r within sensor assembly 10. As can be seen, sensor signals 165 are each provided to meter electronics 20 via communication channel 112.

[0041] Meter electronics 20 includes a processor 210 communicatively coupled to one or more signal processors 220 and one or more memories 230. Processor 210 is also communicatively coupled to user interface 30. Processor 210 is communicatively coupled to a host via a communications port via port 26 and receives power via power port 250. Processor 210 may be a microprocessor, although any suitable processor may be used. For example, processor 210 may be comprised of sub-processors such as a multi-core processor, a serial communications port, a peripheral interface (e.g., a serial peripheral interface), on-chip memory, an I / O port, or the like. In these and other embodiments, processor 210 is configured to perform operations on received and processed signals, such as digitized signals.

[0042] The processor 210 can receive digitized sensor signals from one or more signal processors 220. The processor 210 can also be configured to provide information such as a phase difference, a property of the fluid in the sensor assembly 10, etc. The processor 210 can provide information to a host via a communication port. The processor 210 can also be configured to communicate with one or more memories 230 to receive and / or store information from the one or more memories 230. For example, the processor 210 can receive a calibration coefficient, a sensor assembly zero (e.g., a phase difference for zero flow), and a mass flow correction value from the one or more memories 230. The calibration coefficient, the sensor assembly zero, and the mass flow correction value can be associated with the vibrometer 5 and / or the sensor assembly 10, respectively. The processor 210 can use the calibration coefficient and / or the sensor assembly zero to process the digitized sensor signals received from the one or more signal processors 220 to determine a process value such as density or mass flow rate. The processor 210 can also use the mass flow correction value to correct the mass flow rate determined from the digitized sensor signals.

[0043] The one or more signal processors 220 are shown as including an encoder / decoder (CODEC) 222 and an analog-to-digital converter (ADC) 226. The one or more signal processors 220 may condition analog signals, digitize the conditioned analog signals, and / or provide digitized signals. The CODEC 222 is configured to receive the sensor signals 165 from the left and right pickoff sensors 170l, 170r. The CODEC 222 is also configured to provide the drive signals 185 to the driver 180. In alternative embodiments, more or fewer signal processors may be used.

[0044] As shown, the sensor signal 165 is provided to the CODEC 222 via a signal conditioner 240. The drive signal 185 is provided to the driver 180 via the signal conditioner 240. Although the signal conditioner 240 is shown as a single block, the signal conditioner 240 may be comprised of two or more signal conditioning components, such as an operational amplifier, a filter, e.g., a low-pass filter, and a voltage-current amplifier. For example, the sensor signal 165 may be amplified by a first amplifier, and the drive signal 185 may be amplified by a voltage-current amplifier. The amplification ensures that the magnitude of the sensor signal 165 approximately matches the full-scale range of the CODEC 222.

[0045] In the illustrated embodiment, the one or more memories 230 are comprised of read-only memory 232 (ROM), random access memory (RAM) 234, and ferroelectric random access memory (FRAM®) 236. However, in alternative embodiments, the one or more memories 230 may be comprised of more or less memory. Additionally or alternatively, the one or more memories 230 may be comprised of different types of memory (e.g., volatile, non-volatile, etc.). For example, another type of non-volatile memory, such as an erasable programmable read-only memory (EPROM), may be used in place of FRAM 236. The one or more memories 230 may be storage devices configured to store process data, such as drive or sensor signals, mass flow or density measurements, etc.

[0046] A measurement of mass flow rate can be generated according to the formula:

number

number

[0047] The measured time delay Δt includes an operationally derived (i.e., measured) time delay value that includes the time delay present between pickoff sensor signals, such as the time delay due to the Coriolis effect associated with the mass flow rate through the vibrometer 5. The measured time delay Δt is a direct measurement of the mass flow rate of material passing through the vibrometer 5. The zero-flow time delay Δt0 comprises the time delay at zero flow rate. The zero-flow time delay Δt0 is a zero flow rate that can be determined at the factory and programmed into the vibrometer 5. The zero-flow time delay Δt0 is an exemplary zero-flow value. Other zero-flow values, such as a phase difference, time difference, etc., determined at the zero-flow condition may also be employed. The zero-flow time delay Δt0 may not change even if the flow rate changes. The mass flow rate value of material flowing through the vibrometer 5 is determined by multiplying the difference between the measured time delay Δt and the reference zero-flow value Δt0 by the flow calibration factor FCF. The flow calibration factor FCF is proportional to the physical stiffness of the vibrometer.

[0048] With respect to density, the resonant frequency at which each conduit 130, 130' can vibrate may be a function of the square root of the spring constant of the conduit 130, 130' divided by the total mass of the conduit 130, 130' containing the material. The total mass of the conduit 130, 130' containing the material may be the mass of the conduit 130, 130' plus the mass of the material within the conduit 130, 130'. The mass of the material within the conduit 130, 130' is directly proportional to the density of the material. Therefore, the density of the material may be proportional to the square of the period at which the conduit 130, 130' containing the material vibrates, multiplied by the spring constant of the conduit 130, 130'. Therefore, by determining the period at which the conduit 130, 130' vibrates and scaling the result appropriately, an accurate measure of the density of the material contained within the conduit 130, 130' can be obtained. The meter electronics 20 can determine the period or resonant frequency using the sensor signal 165 and / or the drive signal 185. The conduits 130, 130' can vibrate in multiple vibration modes.

[0049] The vibrometer 5 can be calibrated with a factory zero flow value while the vibrometer 5 is in a no-flow or zero-flow state. A user can additionally and optionally perform a push-button calibration at any time to obtain a push-button zero flow value. Additionally or alternatively, the vibrometer can automatically perform a calibration to obtain an automatic zero flow value. The zero flow value used to measure the fluid flow rate can be a factory zero flow value, a push-button zero flow value, an automatic zero flow value, or any other suitable zero flow value.

[0050] Measurements, stored values / constants, user settings, saved tables, etc. can be used to zero-calibrate the vibrometer 5. Calibration can monitor the vibrometer 5 for conditions and compensate for these conditions. These conditions can include, but are not limited to, user-entered conditions, measured conditions, estimated conditions, etc. These conditions can include temperature, fluid density, flow rate, meter specifications, viscosity, Reynolds number, post-calibration corrections, etc. Additionally, different constants, such as, but not limited to, a flow calibration factor (FCF), can be applied based on operating conditions or user preferences.

[0051] The initial zero flow value may be determined during a calibration performed as part of the initial factory setup of the vibrometer 5. This involves placing the vibrometer 5 in a no-flow or zero-flow state and determining the time delay, phase difference, etc. between the left and right sensor signals 165l, 165r. The determined value is stored in one or more memories 230 as the initial zero flow value and used as the reference zero flow value. For example, in the case of equation [1] above, the reference zero flow value may be the Δt term, which may be the no-flow or zero-flow time delay between the left and right sensor signals 165l, 165r. Once the reference zero flow value is determined, a flow calibration factor (FCF) may be set, which is determined by subtracting the measured time delay Δt from the measured time delay Δt, as can be seen from equation [1] above. measured and mass flow rate

number

[0052] Correction for measured mass flow rate of process gas stream When testing vibrometers, such as Coriolis flowmeters, in a gas test lab, it is not always possible to replicate the exact conditions of the end-use gas and process. Traditionally, vibrometers used in gas flow applications have attempted to use comparisons based on the density, Reynolds number, or mass of the equivalent flowing gas. While these can be useful for other technologies (e.g., orifice plate flowmeters), they are not necessarily the best basis for comparison for vibrometers. To linearize the flowmeter adjustment for optimal measurement accuracy across the entire flow range, Mach number can be used as an input to write a linearization correction function to create a common basis of comparison between the test gas conditions and the application conditions. Alternatively, fluid velocity can be used as a function input when the molecular weight, speed of sound, and chemical composition of the gas are not fully known.

[0053] Vibrometers can optimize gas measurement accuracy by defining a linearization curve based on mass flow rate as an input variable, as long as the gases being measured have similar properties. If gases with significantly different densities may be measured later, optimal measurements can be achieved by linearizing the vibrometer with a correction curve that has velocity as an input variable. Furthermore, because Mach number takes into account not only gas velocity but also gas molecular weight, optimal measurements can be achieved by linearizing the vibrometer with a correction curve that uses Mach number as an input variable. The combination of these parameters allows for better prediction of flow conditions that affect the vibrometer's measurement accuracy.

[0054] Vibrometers are directly affected by flow noise and other conditions in ways unique to gas flows that differ from those of liquid flows. For example, broad white noise and other effects that arise solely from the compressibility of gas-phase flows can interfere with the fundamental measurement signal and cause greater nonlinearity across a flow rate range than typically seen in liquid flows, potentially degrading the measurement. The severity of this effect can be directly tracked with the Mach number, which is determined by the velocity of the gas within the flow tube. Evidence of a decrease in performance (accuracy and repeatability) is observed when the flow tube velocity exceeds a Mach number of 0.2, and a significant decrease in performance is likely to occur above a Mach number of 0.3.

[0055] Typical compensation schemes for vibrometers either use a single meter coefficient (e.g., a flow-weighted average as described in AGA Report No. 11) to apply correction at all flow conditions, or apply a variable correction based on mass flow rate (i.e., a linearized correction curve). Because mass flow rates vary significantly as process conditions change depending on gas type and density, correction curves or data based on mass flow rate are not easily transferable between gases of different composition and / or density. For example, nonlinearities observed in natural gas testing laboratories are less likely to be reproduced in hydrogen measurement applications as a function of mass flow rate than as a function of velocity or Mach number.

[0056] Furthermore, the use of gas as a calibration medium results in a rangeability and maximum flow rate achievable under various conditions, especially for instruments with pressure drop. This is due to the maximum allowable velocity of the fluid through the vibrometer. For example, at lower pressures, the maximum mass flow rate that can pass through the vibrometer is significantly reduced. Therefore, instead of generating a mass error relative to the mass flow rate, the behavior of the instrument can be described in terms of the relationship between the mass error of the gas flow and a parameter related to the fluid velocity, such as the speed of sound or Mach number. The Mach number of a gas is defined as the ratio of the gas velocity to the speed of sound and is given by Equation [2]: M=v / c [2] where: M is the Mach number, v is the fluid velocity, c is the speed of sound in the fluid is.

[0057] Due to the low density of hydrogen (H2), the speed of sound for most alternative gases is lower than that of H2. This allows for a significantly higher maximum mass / volume flow rate for H2 gas at a given Mach number than for most other gases. For example, the flow rate for natural gas at a Mach number of 0.3 with a sonic speed of 466 m / s can be approximately 140 m / s. In contrast, the flow rate for H2 gas at a Mach number of 0.3 with a sonic speed of 1320 m / s can be approximately 396 m / s (2.8 times that of natural gas). The maximum flow rate (Q) of a vibrometer max ) can be set to a Mach number of 0.3 for all gas compositions, which results in different maximum velocities in m / s for different gases (depending on the speed of sound in that gas).

[0058] [Correction method using fluid velocity related parameters] As alluded to above and described in more detail below, a solution to the gas-to-gas transferability, rangeability and maximum flow rate of a vibrometer is to linearize the output of the vibrometer based on the Mach number or fluid velocity of the gas flow by applying a mass flow error correction relationship based on a fluid velocity related parameter, such as Mach number, fluid velocity, etc. The fluid velocity related parameter can be any parameter that is or includes a fluid velocity term.

[0059] In the specific example of Mach number and fluid velocity, if the molecular weight and / or speed of sound of the gas are known from an analysis of the gas's chemical composition, the Mach number may be preferred over the fluid velocity. However, if the gas properties and composition are not known, the fluid velocity method can be employed by simply measuring the mass flow rate and flow density of the gas and applying the known cross-sectional area of ​​the flow meter to the flow tube. Exemplary specific details of these calculations are described below.

[0060] The fluid velocity can be determined using equation [3].

number

number

number

number

[0061] To compensate based on Mach number, a user of a vibrometer, such as the vibrometer 5 described above, may need to input the molecular weight mW and / or speed of sound (SOS) of the calibration or surrogate gas during calibration, and then input the molecular weight and / or SOS of the process gas to be measured after installation of the vibrometer. To calibrate and apply the necessary correction relationship (e.g., function, relationship, curve, ordered pair, etc.) to Mach number, the meter electronics determine a correction factor for each test flow rate based on the flow rate (determined from the mass flow rate, density, and cross-sectional area of ​​the meter) and the Mach number, which is determined by the molecular weight or speed of sound of the calibration gas.

[0062] The mass flow error correction relationship may be formed by any standard method of fitting a curve to the calibration data, whether Mach number based, fluid velocity based, etc., such as linear interpolation between adjacent points or polynomial fitting. Any corrections subsequently applied during process gas measurements may be determined, for example, by a linearization correction algorithm and may be based on fluid velocity, Mach number, or other fluid velocity related parameters, and may be observed and consistent with the errors observed during calibration at the same fluid velocity values, Mach numbers, etc. Meter electronics, such as meter electronics 20 described above, may be configured to calculate the mass flow error correction relationship. a Once v is determined, a lookup table and / or curve is used to find the stored linearized compensation value at any measured Mach number or fluid velocity. This mass flow error compensation value can then be used to compensate the mass flow value, as shown in the following exemplary equation [6]:

number

number

number

[0063] FIG. 3 illustrates meter electronics 20 for determining and using a mass flow error compensation relationship for vibrometer 5. As shown in FIG. 3, meter electronics 20 includes interface 301 and processing system 302. Meter electronics 20 receives a vibration response from a sensor assembly, such as sensor assembly 10. Meter electronics 20 processes the vibration response to obtain flow characteristics of the flow material flowing past sensor assembly 10. Meter electronics 20 may also perform checks, verifications, calibration routines, etc. to ensure that the flow characteristics of the flow material are accurately measured.

[0064] The interface 301 can receive the sensor signal 165 from one of the pickoff sensors 170l, 170r shown in FIGS. 1 and 2. The interface 301 can perform any necessary or desired signal conditioning, such as formatting, amplifying, or buffering in any manner. Alternatively, some or all of the signal conditioning can be performed by the processing system 302. Additionally, the interface 301 can facilitate communication between the meter electronics 20 and an external device. The interface 301 can be electronic, optical, or wireless. The interface 301 can provide information based on the vibration response. The interface 301 can be coupled to a digitizer, such as the CODEC 222 shown in FIG. 2, where the sensor signal includes an analog sensor signal. The digitizer samples and digitizes the analog sensor signal to generate a digitized sensor signal.

[0065] The processing system 302 performs the operations of the meter electronics 20 and processes the flow measurements from the sensor assembly 10. The processing system 302 executes one or more processing routines, thereby processing the flow measurements to generate one or more flow characteristics. The processing system 302 is communicatively coupled to the interface 301 and configured to receive information from the interface 301.

[0066] Processing system 302 can comprise a general-purpose computer, a microprocessing system, a logic circuit, or other general-purpose or customized processing device. Additionally or alternatively, processing system 302 may be distributed across multiple processing devices. Processing system 302 can also include any manner of integrated or separate electronic storage media, such as storage system 304.

[0067] The storage system 304 can store vibrometer parameters and data, software routines, constant values, and variable values. In one embodiment, the storage system 304 includes routines executed by the processing system 302, such as an operation routine 310 for the vibrometer 5, a calibration routine 320, and a correction routine 330. The storage system can also store statistics such as the mean, standard deviation, and confidence interval.

[0068] The operating routine 310 can determine a mass flow value 312 and a density value 314 based on the sensor signals received by the interface 301. The mass flow value 312 can therefore be an uncorrected, directly measured mass flow value, etc. The mass flow value 312 can be determined from the sensor signals, such as the time delay between the left and right pickoff sensor signals. The density value 314 can also be determined from the sensor signals, for example, by determining a frequency from one or both of the left and right pickoff sensor signals.

[0069] The calibration routine 320 may perform the zero verification, flow calibration coefficient determination, and / or mass flow error relationship determination and / or correction described above, although any suitable calibration routine may be used. Accordingly, the calibration routine 320 may determine a plurality of mass flow errors 322. The mass flow errors 322 may be based on mass flow rate and / or based on fluid velocity-related parameters (e.g., Mach number, fluid velocity, etc.). For example, the mass flow errors 322 may comprise one or more relationships, such as two tables, functions, etc., relating mass flow rate and / or Mach number or fluid velocity to mass flow error.

[0070] Storage system 304 is also shown as including a correction routine 330. Correction routine 330 can correct an uncorrected mass flow rate, such as mass flow rate value 312 shown in FIG. 3, using a mass flow error correction relationship 332 to determine a corrected mass flow rate value 334. For example, mass flow error correction relationship 332 can be a function based on mass flow rate error 322 determined by calibration routine 320. Mass flow rate error correction relationship 332 can be based on a fluid velocity-based parameter, such as the Mach number or fluid velocity of the alternative gas flow, as described in more detail below.

[0071] [Measurement error based on mass flow rate vs. fluid velocity relationship] As previously mentioned, alternative gas flows can be used during calibration to determine mass flow error correction relationships that can be used to correct uncorrected mass flow values. However, mass flow error correction relationships based on mass flow rate may not be transferable to other gases. As shown in Figures 4-9 below, mass flow error correction relationships based on fluid velocity-related parameters such as Mach number or fluid velocity may be applicable to other gases, including those with significant and unique mass flow-based nonlinearities due to their high compressibility, such as hydrogen.

[0072] FIG. 4 illustrates a graph 400 demonstrating the absence of a discernible relationship between the mass flow error percentage and the mass flow rate. As shown in FIG. 4, graph 400 includes a mass flow rate axis 410 in units of kilograms per hour (kg / hr) and a mass flow error axis 420 with a unitless percentage scale. The mass flow rate axis 410 ranges from 0.00 to 450 kg / hr, and the mass flow error axis 420 ranges from -1.0 to 1.0%. Graph 400 also includes a mass flow error scatter plot 430 of air at various mass flow rates and pressures. As can be seen from legend 440, the airflows have pressures ranging from 7 bar to 50 bar. As can be seen from mass flow error scatter plot 430 and legend 440, the airflows were tested several times at each pressure.

[0073] FIG. 5 illustrates a graph 500 showing a discernible relationship between mass flow error percentage and a fluid velocity-related parameter. As shown in FIG. 5, graph 500 includes a fluid velocity axis 510 having a unitless Mach number and a mass flow error axis 520 having a unitless percentage scale. The fluid velocity axis 510 ranges from 0.00 to 0.35 Mach numbers, and the mass flow error axis 520 ranges from -1.0 to 1.0%. Graph 500 also includes a mass flow error scatter plot 530 for air at various mass flow rates and pressures. As can be seen from legend 540, the airflow had a pressure range of 7 bar to 50 bar. As can be seen from mass flow error scatter plot 530 and legend 540, the airflow was tested several times at each pressure.

[0074] FIG. 6 illustrates a graph 600 showing a discernible relationship between mass flow error percentage and a fluid velocity-related parameter. As shown in FIG. 6, graph 600 includes a fluid velocity axis 610 having a unitless Mach number scale and a mass flow error axis 620 having a unitless percentage scale. The range of fluid velocity axis 610 is 0.00 to 0.35, and the range of mass flow error axis 620 is -2.0 to 2.0%. Graph 600 also includes a mass flow error scatter plot 630 for air at various mass flow rates and pressures. As can be seen from legend 640, the airflow had a pressure range of 1.3 bar to 20 bar. As can be seen from mass flow error scatter plot 630 and legend 640, the airflow was tested several times at each pressure.

[0075] As can be seen from Figures 4-6, the mass flow error scatter plot 430 shown in Figure 4 does not have a discernible relationship between the mass flow error value and the mass flow value. In contrast, the mass flow error scatter plots 530, 630 shown in Figures 5 and 6 have a much better and more discernible relationship between the mass flow error value and the Mach number. Also, as can be seen from Figures 5 and 6, the relationship between the mass flow error value and the Mach number is discernible across various pressure values ​​for air. Figures 7-9 below demonstrate that the mass flow error correction relationships based on fluid velocity-related parameters such as Mach number and fluid velocity are transferable across different gases.

[0076] Example Corrections for Mass Flow Rate of Process Fluid FIG. 7 illustrates a graph 700 demonstrating the absence of a discernible relationship between mass flow error percentage and mass flow rate. As shown in FIG. 7, graph 700 includes a mass flow rate axis 710 in pounds per minute (lbs / min) and a mass flow rate error axis 720 having a unitless percentage scale. The mass flow rate axis 710 ranges from 0.00 to 500 lbs / min, and the mass flow rate error axis 720 ranges from -1.0 to 1.0%. Graph 700 also includes a mass flow rate error scatter plot 730 for air, natural gas, and carbon dioxide at various mass flow rates and pressures. As can be seen from legend 740, the air stream has a pressure of 900 pounds per square inch gauge (psig), the natural gas has a pressure of 700 psig, and the carbon dioxide has a pressure of 225 psig. As can be seen from the mass flow error scatter plot 730 and legend 740, air, natural gas, and carbon dioxide flows were tested at various mass flow rates up to about 400 lbs / min.

[0077] Similar to the mass flow error scatter plot 430 described with reference to Figure 4, the mass flow error scatter plot 730 shown in Figure 7 also does not have a discernible relationship between the mass flow error values ​​and the mass flow values ​​of different gases. With reference to Figures 8 and 9, it can be seen that for different gases, a discernible relationship exists between the mass flow error values ​​and the fluid velocity-related parameter values, particularly Mach number, and that this discernible relationship allows for the construction of a quantifiable relationship between the mass flow measurement error and the fluid velocity-related parameter.

[0078] FIG. 8 illustrates a graph 800 showing a discernible relationship between mass flow error percentage and fluid velocity-related parameters. As shown in FIG. 8, graph 800 includes a fluid velocity axis 810 having a unitless Mach number and a mass flow error axis 820 having a unitless percentage scale. The range of fluid velocity axis 810 is 0.00 to 0.35, and the range of mass flow error axis 820 is -0.6 to 0.6%. Graph 800 also includes a mass flow error scatter plot 830 for air, natural gas, and carbon dioxide at various fluid velocities and pressures. As can be seen from legend 840, the air flow has a pressure of 900 psig, the natural gas has a pressure of 700 psig, and the carbon dioxide has a pressure of 225 psig. As can be seen from mass flow error scatter plot 830 and legend 840, air, natural gas, and carbon dioxide flows were tested at various fluid velocities up to a Mach number of 0.30. Also shown in Figure 8 is a piecewise linear (PWL) function 850 determined from the regression analysis of the carbon dioxide data. Specifically, the mean value of each group of carbon dioxide mass flow error values ​​at each speed (Mach) value is determined. A line is plotted with each mean value as its endpoint.

[0079] FIG. 9 illustrates a graph 900 showing a discernible relationship between the mass flow error percentage and a fluid velocity-related parameter after a mass flow error correction relationship has been applied. As shown in FIG. 9, graph 900 includes a fluid velocity axis 910 having a unitless Mach number and a mass flow error axis 920 having a unitless percentage scale. The range of fluid velocity axis 910 is 0.00 to 0.35, and the range of mass flow error axis 920 is -0.6 to 0.6%. Graph 900 also includes a mass flow error scatter plot 930 for air, natural gas, and carbon dioxide at various fluid velocities and pressures. As can be seen from legend 940, the air stream has a pressure of 900 psig, the natural gas has a pressure of 700 psig, and the carbon dioxide has a pressure of 225 psig. As can be seen from the mass flow error scatter plot 930 and legend 940, air, natural gas, and carbon dioxide flows were tested at various fluid velocities up to Mach 0.30.

[0080] Mass flow error scatter plot 930 of Figure 9 is obtained by applying PWL function 850 of Figure 8 as a correction function to mass flow error scatter plot 830 of Figure 8. Specifically, the value of PWL function 850 is subtracted from the value or values ​​of mass flow error scatter plot 830. As can be seen from Figure 9, mass flow error scatter plot 930 has mass flow error values ​​that are less than 0.4%, and in most cases less than 0.2%.

[0081] Although PWL function 850 is determined by averaging carbon dioxide, any suitable means for determining the appropriate relationship between mass flow error and fluid velocity-related parameter may be employed, e.g., one or more functions, a table of ordered pairs, etc. For example, an alternative function may be a PWL function having endpoints determined by averaging the mass flow error values ​​of all gases within a range of fluid velocity-related parameter values. By way of example, as shown in FIG. 8, natural gas and air are frequently measured at approximately the same Mach number. Additionally or alternatively, the alternative function and / or ordered pairs may be nonlinearly based and / or determined by using nonlinear regression, such as, for example, one or more polynomial functions and / or polynomial regression.

[0082] As can be seen from the foregoing discussion, determining a mass flow error relationship may require determining a "known" mass flow rate. The known mass flow rate may be provided, for example, by a reference flow meter, a source providing a gas flow rate within a very narrow range of a setpoint, and / or the like. These and other devices may be collectively referred to as reference devices. The reference device may be in series with a vibrometer, such as the vibrometer 5 described above. Thus, the reference device may provide a known or reference mass flow rate and / or fluid velocity-related parameter value that can be used to calibrate the vibrometer in series. Exemplary systems utilizing reference devices are described below.

[0083] [system] FIG. 10 illustrates a system 1000 for determining a vibrometer mass flow error correction relationship. As illustrated in FIG. 10, the system 1000 includes the vibrometer 5 described above, although any suitable vibrometer can be used. The vibrometer 5 is shown in series fluid communication with a reference device 1010. That is, the reference device 1010 and the vibrometer 5 carry the same gas flow. Therefore, a reasonable assumption can be made that the measurements of the gas flow parameter measured by the vibrometer 5 and the reference device 1010 should be the same. Furthermore, a reasonable assumption can be made that any difference between the measurements of the parameter determined by the vibrometer 5 and the reference device 1010 is due to measurement error by the vibrometer 5.

[0084] 10 , system 1000 includes a calibration circuit 1020 communicatively connected to vibrometer 5 and reference device 1010. Calibration circuit 1020 is shown with dashed lines to indicate that calibration circuit 1020 may or may not be separate from, and may or may not be integrated with, vibrometer 5 and / or reference device 1010. Regardless of geometric factors, calibration circuit 1020 is capable of determining the difference between measurements of a parameter of a gas flow provided by vibrometer 5 and reference device 1010.

[0085] The difference between the measurements of the gas flow parameter may be the measured mass flow difference between the mass flow values ​​provided by the vibrometer 5 and the reference device 1010, which may be referred to as the measured mass flow difference. The measured mass flow difference is, for example, divided by the mass flow value provided by the reference device and multiplied by 100 to determine a percentage mass flow error value.

[0086] Additionally, the calibration circuit 1020 can obtain fluid flow rate or fluid velocity related parameters from the reference device 1010 and / or the vibrometer 5. By way of example, the calibration circuit 1020 can obtain mass flow rate and / or fluid velocity related parameters, such as the fluid velocity and / or Mach number of the gas flow, e.g., from the reference device 1010. Thus, the calibration circuit 1020 can calculate and determine a plurality of mass flow rate errors of the vibrometer 5 at a corresponding plurality of mass flow rate and / or fluid velocity related parameter values.

[0087] The calibration circuitry 1020 may also determine functions, ordered pairs of values, and / or the like relating mass flow rate values ​​and / or fluid velocity-related parameter values, such as fluid velocity values ​​or Mach numbers, to mass flow rate error correction values, as described above with reference to Figure 9. Thus, the system 1000, or in particular the reference device 1010, whether stand-alone or integrated with the vibrometer 5 and / or the reference device 1010, may provide one or more functions, ordered pairs of values, and / or the like that can be used to correct the measured mass flow rate error of the vibrometer 5. Exemplary methods for doing this are described in detail below.

[0088] [method] 11 illustrates a method 1100 for determining a mass flow error correction relationship for a vibrometer, such as vibrometer 5 described above. As shown in FIG. 11, method 1100 compares each of a plurality of mass flow measurement values ​​for an alternate gas flow to each of a plurality of reference mass flow measurement values ​​for the corresponding alternate gas flow, at step 1110. At step 1120, method 1100 determines a plurality of mass flow measurement errors corresponding to a plurality of fluid velocity-related parameter values ​​for the alternate gas flow based on these comparisons.

[0089] As described above with reference to Figure 10, the plurality of reference mass flow measurements may be determined and provided by a reference device, such as the reference device 1010 described with reference to Figure 10. Thus, for example, a system 1000 comprising a vibrometer 5 configured to measure the mass flow rate of an alternative gas flow, a reference device 1010 disposed in series with the vibrometer 5, and a calibration circuit 1020 in communication with the vibrometer 5 and the reference device 1010 may perform the steps of the method 1100.

[0090] For example, for an alternative gas flow, the vibrometer 5 can determine a mass flow measurement and the reference device 1010 can determine a reference mass flow rate. Thus, multiple reference mass flow measurements of the alternative gas flow can be provided by the reference device 1010 in series with the vibrometer 5. The calibration circuit 1020 can use the mass flow measurements of the alternative gas flow and the reference mass flow rate configured to implement the method 1100.

[0091] As can be understood from the above description, the plurality of fluid velocity-related parameter values ​​for the alternative gas flow may include one of a plurality of fluid velocity values ​​and a plurality of Mach number values ​​for the alternative gas flow. The alternative gas flow may include air, natural gas, carbon dioxide, nitrogen, and / or helium. As the foregoing description of Figures 8 and 9 indicates, the plurality of mass flow measurement errors and resulting mass flow error correction relationships are transferable to other gases, such as hydrogen. The plurality of mass flow measurement errors corresponding to the plurality of fluid velocity-related parameter values ​​for the alternative gas flow may include a plurality of differences between each of the plurality of mass flow measurement values ​​and each of the plurality of corresponding reference mass flow measurement values.

[0092] Method 1100 may further include additional steps. For example, method 1100 may include flowing the alternative gas flow through a vibrometer 5, although any suitable vibrometer may be used. The vibrometer may thus provide a plurality of mass flow measurements. Additionally or alternatively, method 1100 may further include using the vibrometer 5 to determine a plurality of mass flow measurements at a corresponding plurality of fluid velocity-related parameter values ​​for the alternative gas flow. This may include calculating the fluid velocity-related parameter values ​​according to equations [2]-[5] above, although any suitable equation may be employed.

[0093] Additionally, the method 1100 can store the mass flow measurement errors as ordered pairs of the mass flow measurement errors and corresponding fluid velocity-related parameter values ​​in the meter electronics of the vibrometer, such as the meter electronics 20 of the vibrometer 5 described above. Thus, the meter electronics can later determine the mass flow error correction relationships, such as after the vibrometer 5 is installed for a process application.

[0094] The method 1100 may further determine a mass flow error correction relationship based on the plurality of mass flow measurement errors and the corresponding plurality of fluid velocity-related parameter values ​​and store the mass flow error correction relationship in the vibrometer. For example, the calibration circuit 1020, whether stand-alone or within the vibrometer and / or reference device 1010, may determine the mass flow error correction relationship and store the mass flow error correction relationship in the meter electronics of the vibrometer.

[0095] As can be appreciated, the stored mass flow error values ​​and / or mass flow error correction relationships can be used to correct the measured mass flow values ​​of the process gas measured by the vibrometer. As can be appreciated from the foregoing description, the mass flow error values ​​and / or mass flow error correction relationships can be for alternate gases and still be used to correct the measured mass flow rate of the process gas.

[0096] 12 illustrates a method 1200 for using a mass flow error correction relationship with a vibrometer, such as vibrometer 5 described above. As shown in FIG. 12, method 1200 determines a fluid velocity-related parameter value for the process gas flow based on the measured mass flow rate value, density value, and cross-sectional area of ​​the process gas flow at step 1210. At step 1220, method 1200 determines a mass flow error correction value based on the fluid velocity-related parameter value.

[0097] As can be appreciated, method 1200 can be performed by suitable meter electronics of a vibrometer, such as meter electronics 20 of vibrometer 5 described above. Referring to FIGS. 1-3 , vibrometer 5 includes a storage system 304 and a processing system 302 communicatively coupled to storage system 304. Processing system 302 can be configured to perform method 1200. One or more values ​​related to the process gas flow, such as the density or cross-sectional area of ​​the process gas flow, may be measured by sensor assembly 10, input by a user, provided by other devices, and / or the like, for example.

[0098] In step 1220, determining a mass flow error correction value based on the fluid velocity-related parameter value can include obtaining a mass flow error correction relationship for the alternative gas flow and determining a mass flow correction value based on the mass flow error correction relationship for the alternative gas flow and the fluid velocity-related parameter value. The fluid velocity-related parameter value can include one of a fluid velocity value and a Mach number value for the process gas flow. As described above with reference to FIG. 11, the alternative gas flow can include one of air, natural gas, carbon dioxide, nitrogen, and helium. As explained above, the mass flow error correction relationship can be transferred to other gases, so the process gas flow can be a gas having a different compressibility factor, such as a hydrogen gas flow.

[0099] Method 1200 can include additional steps. For example, method 1200 can further measure the mass flow rate of the process gas stream with a vibrometer to determine a measured mass flow rate value. Additionally or alternatively, method 1200 can correct the measured mass flow rate value with a mass flow error correction value.

[0100] The vibrometer 5, meter electronics 20, system 1000, and methods 1100 and 1200 described above can determine and use mass flow error correction relationships. For example, method 1100 determines a mass flow error correction relationship based on a fluid velocity-related parameter of an alternative gas flow. Because the mass flow error correction relationship is based on a fluid velocity-related parameter, the mass flow measurement error, and more specifically, the mass flow error correction relationship, is transferable from the alternative gas flow to other gas flows. For example, nonlinearities between different gas flows are typically not similar even when the Mach numbers are similar. This is believed to be due to the fact that the compressibility of various gases is taken into account when using Mach numbers. Thus, the measured mass flow rate of a highly compressible gas, such as hydrogen, can be corrected based on the mass flow measurement error of a gas that is relatively less compressible, more readily available, and less expensive, such as air, carbon dioxide, or natural gas.

[0101] Furthermore, the vibrometer 5 can advantageously set a range for mass flow measurement errors based on fluid velocity-related parameters. For example, as noted above, vibrometers such as the vibrometer 5 described above typically exhibit unacceptable signal noise at gas flows with Mach numbers above 0.30. However, highly compressible gases tend to have relatively high sonic velocities. As a result, a given mass flow rate for a highly compressible gas may result in a lower Mach number than a gas with a more typical sonic velocities. Thus, the vibrometer 5 can measure highly compressible gases at relatively high mass flow rates without experiencing signal noise. As an example, the vibrometer 5 can be evaluated to be capable of measuring the mass flow rate of hydrogen, for example, at a mass flow rate three times that of a non-highly compressible gas.

[0102] The detailed descriptions of the above embodiments are not exhaustive descriptions of all embodiments contemplated by the inventors as falling within the scope of the present specification. Indeed, those skilled in the art will recognize that certain elements of the above embodiments can be combined or deleted in various ways to create additional embodiments, and that such additional embodiments will fall within the scope and teachings of the present specification. It will also be apparent to those skilled in the art that the above embodiments can be combined, in whole or in part, to create additional embodiments that fall within the scope and teachings of the present specification.

[0103] Thus, while specific embodiments are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the present disclosure, as will be recognized by those skilled in the art. The teachings provided herein may be applied to other vibrometers, meter electronics, and methods for determining and using a vibrometer mass flow error correction relationship, in addition to the embodiments described above and illustrated in the accompanying drawings. Accordingly, the scope of the above-described embodiments should be determined from the following claims.

Claims

1. 1. A method for determining a mass flow error correction value for a vibrometer, comprising: comparing each of a plurality of mass flow measurements of the alternative gas flow to a corresponding plurality of reference mass flow measurements of the alternative gas flow; determining a plurality of mass flow measurement errors corresponding to a plurality of fluid velocity-related parameter values ​​for the alternative gas flow based on the comparison; A method comprising:

2. The method of claim 1 , wherein the plurality of fluid velocity related parameter values ​​of the alternative gas flow comprises one of a plurality of fluid velocity values ​​and a plurality of Mach number values ​​of the alternative gas flow.

3. The method of claim 1 or 2, wherein the plurality of reference mass flow measurements of the alternative gas flow are provided by a reference device disposed in series with the vibrometer.

4. 4. The method of claim 1, wherein the alternative gas stream comprises one of air, natural gas, carbon dioxide, nitrogen, and helium.

5. 5. The method of claim 1, wherein the plurality of mass flow measurement errors corresponding to the plurality of fluid velocity-related parameter values ​​of the alternative gas flow comprise a plurality of differences between each of the plurality of mass flow measurement values ​​and a corresponding one of the plurality of reference mass flow measurement values.

6. The method of claim 1 , further comprising flowing the alternative gas flow through the vibrometer.

7. 7. The method of claim 1, further comprising using the vibrometer to determine the plurality of mass flow measurements at a corresponding plurality of fluid velocity-related parameter values ​​of the alternative gas flow.

8. 8. The method of claim 1, further comprising storing the plurality of mass flow measurement errors as a plurality of ordered pairs of the plurality of mass flow measurement errors and a corresponding plurality of the fluid velocity-related parameter values ​​in meter electronics of the vibrometer.

9. 9. The method of claim 1, further comprising determining a mass flow error correction relationship based on the plurality of mass flow measurement errors and the corresponding plurality of fluid velocity-related parameter values, and storing the mass flow error correction relationship in the vibrometer.

10. 1. A system (1000) for determining a mass flow error correction relationship for a vibrometer (5), comprising: said vibrometer (5) configured to measure the mass flow rate of an alternative gas flow; a reference device (1010) arranged in series with the vibrometer (5) and configured to determine a reference mass flow rate of the alternative gas flow; and A calibration circuit (1020) in communication with the vibrometer (5) and the reference device (1010), the calibration circuit (1020) being configured to perform the method of any one of claims 1 to 9. A system (1000) comprising:

11. 1. A method of using a vibrometer mass flow error correction relationship, comprising: determining a fluid velocity-related parameter value for the process gas flow based on the measured mass flow rate value, density value, and cross-sectional area of ​​the process gas flow; determining a mass flow error correction value based on the fluid velocity-related parameter value; A method comprising:

12. The method of claim 11 , wherein the fluid velocity related parameter value comprises one of a fluid velocity value and a Mach number value of the process gas flow.

13. 13. The method of claim 11 or 12, wherein the process gas stream is a hydrogen gas stream.

14. 14. The method of claim 11, further comprising measuring a mass flow rate of the process gas flow using the vibrometer to determine the measured mass flow rate value.

15. 15. The method of claim 11, further comprising correcting the measured mass flow value with the mass flow error correction value.

16. determining the mass flow error correction value based on the fluid velocity related parameter value; obtaining a mass flow error correction relationship for the alternative gas flow; determining the mass flow correction value based on the mass flow error correction relationship and the fluid velocity-related parameter value for the alternate gas flow; 16. The method of any one of claims 11 to 15, comprising:

17. 17. The method of claim 16, wherein the alternative gas stream comprises one of air, natural gas, carbon dioxide, nitrogen, and helium.

18. 1. A meter electronics system (20) using a mass flow error correction relationship, comprising: a storage system (304); a processing system (302) communicatively connected to the storage system (304), the processing system (302) configured to perform the method of any one of claims 11 to 17; meter electronics (20).

19. A vibrometer (5) using a mass flow error correction relationship, a sensor assembly (10) configured to measure the mass flow rate of a process gas stream; 19. Meter electronics (20) communicatively coupled to the sensor assembly (10), the meter electronics (20) being provided in accordance with claim 18; A vibration meter (5).

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