Ensuring metrological traceability of the gas flow measurements at high pressure in Ukraine

Described is the PVTt primary measurement standard used to calibrate primary standard critical flow nozzles with throat diameters from 2 mm to 8 mm over a flow rate range of 100 m 3 /h up to 1800 m 3 /h. Means and methods of the working standard critical flow nozzles calibration are considered. The metrological traceability chain for the gas flow measurements is presented. In the metrological traceability chain, the primary standards are the primary standard critical flow nozzles, the metrological characteristics of which are established through calibration using the primary measuring system and the primary measurement procedure. The secondary standards are working standard critical flow nozzles, the metrological characteristics of which are established by comparing them with primary standard noz - zles. The metrological traceability chain has a branched structure, as the measurement model includes various physical quantities: pressure, temperature, volume, time, and gas properties.


Introduction
Metrological traceability is one of the most important aspects of the measurement result quality.

Traceability of the results to a common metrological
reference is a necessary condition for their metrological comparability [1] .
In general, the metrological reference has three components: measurement standards, units of measurement, and measurement methods.In the field of gas flow measurement, critical flow nozzles are often used as standard measures ensuring metrological traceability of flow rate measurements at high pressure [2,3] .In the critical flow mode, the gas mass flow rate through the nozzle depends only on the gas pressure and temperature at the nozzle inlet and the gas thermodynamic properties.The nozzles have no moving parts, are insensitive to shocks, and provide high flow rate stability.Requirements on design and methods of using critical flow nozzles for gas flow rate measurement are outlined in [2,3] .
In gas flow rate measurements, the results are expressed in the units of volume (m 3 /h) or mass The standard consists of four units: gas preparation unit, gas flow formation unit, calibration unit for primary standard nozzles, and calibration unit for working standard nozzles.
The gas preparation unit contains a set of technical means for gas compression, purification, storage, and quality control: membrane and piston compressors, vacuum pumps, universal gas purification and drying units, and containers for prepared gases.
The gas flow formation unit (Fig. 1) is designed to create a stationary single-phase gas flow that ac- The metrological traceability chain is implemented through a sequence of nozzles.Primary standard nozzles are calibrated using primary gas flow rate standards that can be based on different methods -volumetric, gravimetric, or PVTt.By using the latter, it is possible to reproduce a flow rate unit over the wide ranges of pressure and gas flow rate.Metrological characteristics of the PVTt standards maintained in various countries are considered in [4,5] .
According to the method applied, the calibration procedures for the primary critical flow nozzles are developed.For working critical flow nozzles, procedures are established for their calibration by comparison with primary nozzles using appropriate measuring systems.

The primary measurement standard of gas flow rate
At the SE «Ukrmetrteststandart», work is underway to create a PVTt measurement standard for calibrating critical flow nozzles with a throat diameter from 2 mm to 8 mm over the flow rate range from 100 m 3 /h up to 1800 m 3 /h.Characteristics and parameters of the standard were given in [5] : -gas source capacity (dry air, nitrogen) -16,66 m The working standard nozzle calibration unit (Fig. 3) is a comparator based on a TRZ turbine meter and a G-400 Delta rotary meter and contains a set of primary standard nozzles with throat diameters from 2 mm to 8 mm.

Metrological traceability chain
The link of the gas flow measurement result to the primary standard of the volume flow rate unit is established through a sequence of measurement standards and calibrations, which ensures the operation of the primary standard dissemination system based on metrological traceability.
In the metrological traceability chain shown in Fig. 4, the primary standard critical flow nozzles are the primary standards, and their metrological characteristics are established through calibration using the primary measuring system and the primary measurement procedure [6,7] .Working standard critical flow nozzles are the secondary standards, and their metrological characteristics are established through calibration using a measuring system and measurement procedure for working standard nozzles.
It is worth noting that according to [3] , the «primary calibration procedure» can be the calculation procedure established by this standard, and in [3] it is called «dry calibration».The mass flow rate of gas is calculated by the formula: where A is a cross-sectional area of the nozzle throat; C d is a discharge coefficient; C * is a critical flow function; p 0 is an absolute stagnation pressure of the gas at the nozzle inlet; T 0 is an absolute stagnation temperature of the gas at the nozzle inlet; M is a molar mass of gas; R is a universal gas constant.The primary standard nozzle calibration unit (Fig. 2) contains a collection vessel, a piston gas pres- Voltage, V 1 2 Temperature, K Pressure, P The cross-sectional area of the nozzle throat is calculated from the diameter of the throat, d n , by the formula: and the discharge coefficient -by the formula: where a, b, c, d, e, f , n are the coefficients, the values of which are given in [3] for the nozzles with toroidal and cylindrical throats, and Re is a Reyn- olds number: where µ is a gas dynamic viscosity.
There are several input quantities in this measurement model, and the value of each of them must be metrologically traceable, thus, the metrological traceability chain for the measurand, mass flow, has a branched form.Traceability to the units of length, pressure, and temperature is obvious since these quantities are present in equations ( 1), (2), and (4) ex- plicitly.The measurement model also includes gas mass M [3] : as well as gas dynamic viscosity through equation ( 4).
According to [7] , «Where the input quantity in a measurement model is a conversion factor such as molar mass» (and in our case, there are also other properties of the substance), the requirement for metrological traceability also applies the values of these quantities, but it can be assumed that metrological traceability for them has been already established.So, to document metrological traceability, it is sufficient to refer to recognized sources, such as the IUPAC atomic mass tables.As a source of the physical properties data for the calculation of the gas mass flow rate through the nozzle, the REFPROP may be used, which is a database of standard reference data on thermodynamic and transport properties of substances, developed and maintained by the US National Institute of Standards (NIST) [8] .
The peculiarity of equation ( 1) is that the discharge coefficient C d on its right-hand side depends on the Reynolds number Re, which in turn is calcu- lated through the gas mass flow rate, q m , which stands on the left side of the equation.In its general form, equation ( 1) can be expressed as: where k is a parameter depending on the size of the nozzle throat, gas properties, and flow stagnation conditions, and f q m ( ) is a certain function of q m .Such equations can be solved by the itera- tion method.The algorithm for calculating the gas flow rate through the critical flow nozzle for a given nozzle throat diameter, parameters of state, and gas properties were implemented us-ing EXCEL spreadsheets.Data on gas properties at given temperature and pressure values, as well as gas molar mass, were taken from the REFPROP database [8] .In the first version of the program, the discharge coefficient C d was cal- culated by the formulae from the then-current version of the ISO 9300:2005 standard [2] .These formulae differ from formula (3) from the standard [3] .For a nozzle with a toroidal throat, the difference between the calculations by the formulae from [2] and [3] was 0,005 % to 3 % over the range of Reynolds number of 2,3•10 4 to 1,3•10 7 .
According to [3] , for the nozzles manufactured exactly to the requirements of this standard, the relative expanded uncertainty of the discharge coefficient C d calculated by formula ( 3) is 0,3 % at a confidence level of 95 %.If take into account the other sources of uncertainty, it becomes obvious that «dry calibration», i.e., calculating the gas flow from the nozzle throat diameter, temperature, pressure, and gas properties, will not provide the accuracy required at a high standard level.Therefore, to ensure the high-level needs, nozzles are calibrated experimentally.In [3] , this is called «flow calibration».
The most common way to calibrate nozzles at different inlet pressures is the PVTt method.Let us consider a simplified measurement model for the nozzle calibration by the PVTt method.
The gas mass flow rate during the experiment, q m , is determined by the equation: where m g is the mass of the gas that entered the collec- tion vessel during the experiment over the time interval τ .
Mass m g is determined as the difference: where m f and m 0 are masses of the gas in the collec- tion vessel at the final and start moments of filling, respectively.
The masses on the right-hand side of equation ( 8) can be expressed in terms of the collection vessel volume and gas density according to the equa- where V ct is an internal volume of the collection ves- sel; ρ f and ρ 0 are the gas densities in the collection vessel at the final and start moments of filling, respectively.
The gas density can be determined by the equation of state of a real gas through the parameters of state (pressure, temperature), molar mass, and compressibility factor: where p f and p 0 are the absolute gas pressures in the collection vessel at the final and start moments of filling, respectively; T f and T 0 are the absolute temperatures of the gas in the collection vessel at the final and start moments of filling, respectively; z f and z 0 are the gas compressibility factors at the collection vessel conditions at the final and start moments of filling, respectively; M is a molar mass of the gas; R is a universal gas constant.
By combining equations ( 7) -( 12), we obtain the equation for the gas mass flow rate: Obviously, such a measurement model implies traceability to the units of pressure, temperature, time, and data on the compressibility factor at a given temperature and pressure, as well as gas molar mass, which can be taken from the REFPROP database [8] .In Fig. 4, another branch of traceability to a unit of electric voltage is shown; this is due to the use of thermoelectric transducers for temperature measurement.
Let us consider separately the metrological traceability of the collection vessel volume value V ct .The V ct can be determined in two ways: by gravimet- ric method and volume expansion method [9] .In the first case, the volume is determined by the mass of gas or water that fills the collection vessel and their density, thus, there is a direct traceability to the unit of mass, but also to the standard reference data on properties.Moreover, for accurate weighing, the buoyancy effect must be taken into account, and thus, a term containing the air density under weighing conditions appears in the measurement model.
The CIPM-2007 equation [10] is a generally accepted source of data on air density depending on temperature, atmospheric pressure, and humidity.
The essence of the second volume expansion method is that a container of a known volume is filled with gas under pressure, and a container of unknown internal volume, i.e., a collection vessel, is evacuated.
Then, the two containers are connected, and based on the change in gas density in both containers and the known capacity of one of them, the capacity of the other is calculated.So, the issue of the traceability of the collection vessel measured volume is reduced to the traceability of the value of the «known volume» (and again of the gas density values).The «known volume» is usually measured by the gravimetric method, which provides the highest accuracy, and the metrological traceability of the results obtained by this method has been discussed above.
As already mentioned, the measurement model for the nozzle calibration by the PVTt method, according to equations ( 7) -( 13), is simplified.In real setups, besides, to the collection vessel, there are additional volumes filled with gas during the experiment, and these volumes must be taken into account in the measurement model.In principle, they can be determined by one of the two methods described here, but given their small contribution to the overall flow rate measurement uncertainty budget, these volumes can also be calculated from the corresponding geometric dimensions.In this case, another branch appears in the traceability chain up to a unit of length.
There is another aspect of metrological traceability that is not so obvious, but it should also be kept in mind.All the gas properties discussed above depend on the gas composition.Even when the experiment is conducted with «pure» gases, certain requirements are put forward for their purity, in other words, the permissible content of impurities is specified.This shows the need to provide metrological traceability to the unit of gas component mole fraction.
Summing up, we can say that the metrological traceability chain for the gas mass and volume flow rate measurements obtained with the primary measuring system according to the primary measurement procedure is a branched one and includes traceability routes to the units of mass, pressure, temperature, time, electric voltage, length, and molar fraction of components (the last two are not shown in Fig. 4).

Calibration of the working standard nozzles
Working standard nozzles are calibrated by comparison with primary standard nozzles using a comparator based on turbine and rotary gas flowmeters with high-frequency output [5] .The working standard nozzle calibration unit is shown in Fig. 3.
The gas volume flow rate through the working standard nozzle is calculated using an equation based on the assumption that the frequency response of gas meters to the flow rate is linear: where Q p is a volume flow rate of gas through the work- ing standard nozzle; Q n is a volume flow rate through the primary standard nozzle; f n is a pulse frequency of the meter output sig- nal while gas passing through the primary stan- Formation of the stationary flow and the nozzle calibration process are automated using a control system that includes a programmable logic controller (PLC), input/output modules, and a frequency counter unit.
The PLC is programmed to control the external peripheral valves by generating control commands to the input/output modules.
The frequency counter unit counts the time and generates measurement start and end commands.
The actual values of the controlled parameters and the status of the peripheral devices are visualized by a computer connected to the PLC using the unified digital protocol.

(
kg/h) flow rate.By the underlying physical principle, the critical flow nozzles reproduce a unit of gas mass flow rate, thus, the results of their calibration are usually expressed in terms of mass flow rate.At the same time, in trade and financial transactions, statistical reports, etc., the volume flow rate values are traditionally used.When necessary, the critical flow nozzle calibration results, expressed in terms of mass flow rate, are converted to volume flow rate, celerates in the nozzle throat to a critical speed (local speed of sound).The flow forming unit contains two pressure reducers -HON 214 and HON 200 combined with an RMG 650 pilot, two safety valves -HON 873 and RMG 704 with actuator HON 670, a thermostat, and two tube heaters.The gas enters the stationary flow forming unit at a pressure of 150 bar, and after two-stage pressure reduction and termination of irreversible thermodynamic processes in the system, it enters the primary nozzle calibration unit under the pressure of (10-50) bar.The first pressure drop from 150 bar to 100 bar is effected by a direct-acting pressure reducer HON 214, and the second pressure drop, from 100 bar to an operating pressure ranging from 10 bar to 50 bar, is achieved using pilot-operated pressure reducer HON 200.Due to the Joule-Thompson effect, the gas pressure drop leads to a temperature decrease of about 0,5 °C per 1 bar, therefore, tubular heaters are installed upstream of each reducer, which ensures the stability of the flow temperature downstream the reducers within (20±2) °С.For the safety of unit operation, two safety valves are installed in it: HON 873 relief valve and RMG 704 shut-off valve with an actuator HON 670.The HON 200 pressure reducer is equipped with two pilots, RMG 650 and RMG 650-1, providing operation over the pressure ranges of (10-40) bar and (20-90) bar.Pressure regulation errors are due to the design of pressure reducers and are affected by the input pressure, gas flow rate, and flow resistance in the outlet channels, which increase with increasing flow rate.usually reduced to standard conditions.(It can also be noted that for each specific critical flow nozzle, the gas volume flow rate reduced to the nozzle inlet conditions will remain almost unchanged for any inlet temperature and pressure, and a certain variability of this reduced flow rate is associated with gas non-ideality and the dependence of the discharge coefficient on the Reynolds number -see formula (3) below).

Fig. 4 .
Fig. 4. Metrological traceability chain for the measurements of the gas volume flow rate at the pressure of (10-50) bar over the range up to 1800 m 3 /h dard nozzle; f p is the pulse frequency of the meter output sig- nal while gas passing through the working standard nozzle.While calibrating working standard nozzles, their nominal flow rate should not differ by more than 10 % from the flow rate through the primary standard nozzles they are compared with.First, gas is passed sequentially through the selected flow meter and the primary standard nozzle, and the pulse frequency of the flow meter output signal f n is measured.Then, the pulse frequency of the flow meter output signal f p is measured while gas passes through the working standard nozzle, and the flow rate through the working standard nozzle is calculated by the equation (14).

1 .
Work continues on creating a PVTt standard for calibration of the critical flow nozzles with a throat diameter of 2 mm to 8 mm over the flow rate range from 100 m 3 /h up to 1800 m 3 /h.