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A three-way pulse method for a precision sound velocity measurement cell
Abstract
Ultrasonic gas flow meters for volumetric flow rate fiscal metering of natural gas (USMs) may possibly also be used for mass and energy flow rate measurement, partially based on sound velocity measurement. To establish the accuracy of the sound velocity measurements given by the USM, and for traceability purposes, an independent high-accuracy sound velocity measurement cell may serve as reference. To include dispersion effects, the cell should preferably work in the operational frequency range of USMs, i.e. 100 - 200 kHz, with natural gas under high pressure. Highly accurate sound velocity cells are available in the audio frequency range, however, less work have demonstrated sufficient accuracy in the 100 - 200 kHz range. Three transient methods are investigated as part of the sound velocity cell development [Proc. 2005 IEEE Ultrasonics Symposium, pp. 1443-1447, 2005]; the methods are seen to have several common sources of experimental uncertainty. In the present work, a three-way pulse method (3PM) is considered as a candidate for the sound velocity cell, and sound velocity results obtained in a prototype cell, containing air at about 1 atm and 27 degC are presented. The results are compared with output from a sound velocity model for air, including dispersion [J. Acoust. Soc. Amer. 93 (5), pp. 2510-2516, 1993]. The results indicate that the 3PM may have potentials to perform in line with the target specifications of the sound velocity cell, i.e. 100-200 ppm, in the frequency range of USMs, 100-200 kHz. Use of a temperature regulated bath is expected to significantly reduce the temperature induced convection flows presently limiting the accuracy of the cell, and to reduce the measurement uncertainty accordingly
... 5 Piston-type diffraction correction models are the most common, based on analytical expressions for radiation from a baffled piston source and extended with reflection models when used for pulse-echo and multiple-reflection measurements. [4][5][6][7][8][9][10][11][12][15][16][17][18][19] The accuracy of such simplified models is related to how close the measurement system at hand resembles that assumed in the model used, 1,4,6 e.g., with respect to the vibration of the transmitter and uniform sensitivity of the receiver. Several authors point to the limitations of piston-type models, 6,12,20,21 emphasizing the need for more accurate modeling of the diffraction correction, which would also help assess the accuracy of piston-type models. ...
... An application area where this would be of interest is sound velocity measurements in fluids using (i) two-distance pulse-echo methods, 4,12,[22][23][24][25] (ii) pulse-echo-overlap methods, 4,26,27 (iii) a combination of one-way and pulse-echo measurements, 10,28 and (iv) a combination of one-way and three-way transmit-receive measurements. 6,[8][9][10][11] Other application areas include absorption measurements in gas 11 and medical ultrasound. 5,14,16 The works cited under (i)-(iv) use piezoelectric transducers that operate at frequencies ranging from the lower hundreds of kilohertz to multiple megahertz, and they all use either coaxially aligned transducers or plane reflectors parallel to the transducer's front face. ...
... An alternative approach is to model the reflector as a new baffled piston source, 5,[8][9][10][11]13,14,17,32 here denoted the new-source model. This is succinctly described by Krautkr€ amer and Krautkr€ amer: 17 "The echo wave produced by a circular disc relector can be analysed most conveniently if we first consider a small circular disk placed on the axis at a great distance from the radiator. ...
In high-precision ultrasonic measurement systems, diffraction correction models accounting for electrical and mechanical boundary conditions may be needed, as shown in prior work using a finite element diffraction correction (FEDC) model for one-way transmit-receive systems. Such descriptions may also be needed for pulse-echo and multiple-reflection ultrasonic measurement applications. The FEDC model is here generalized to n-way measurement systems (n = 1, 2, 3,…) using coaxially aligned piezoelectric transducers in a fluid medium. Comparisons are made with existing diffraction correction models, based on baffled-piston theory combined with (i) specular reflection or (ii) reflection modeled as radiation from a “new source.” Numerical results are given for an example system with two identical cylindrical piezoelectric disks, operating in a fluid medium at ambient conditions. The piston-type diffraction correction models deviate notably from the FEDC model both in the near- and far-fields, and also from each other. The deviations are expected to be application-specific and depend, e.g., on the reflector-to-sound-beam diameter ratio, distance, frequency, and the transducers' vibration patterns. The results show that accurate description of the diffraction effects, such as the one provided by the FEDC model, may be needed in high-precision ultrasonic measurement systems.
... The 3-way pulse method (3PM) and another candidate method for a high-pressure and high-precision VOS cell, here referred to as the "2-way pulse-echo method" (2PEM) [9], have been investigated experimentally and theoretically in refs. [10][11][12][13][14][15], in air at atmospheric and room temperature conditions. A low-pressure VOS cell was constructed and used for this purpose, in which both methods could be applied, cf. ...
... The deviations between the measured and the theoretical VOS were found to be less than 180 ppm, which appears to be encouraging. However, the accuracy of this theoretical model is unfortunately expected to be relatively moderate, of the order of 300 ppm [12]. The accuracy of the measurements are thus difficult to quantify from this comparison. ...
... Attempts were made to establish an uncertainty budget for the VOS measurements made. However, in both methods, the diffraction correction appears to be the largest and most important correction, and since the uncertainty of this diffraction correction (which is expected to dominate the uncertainty budget) has so far been difficult to specify, no complete uncertainty budget was established in [10][11][12][13][14][15]. Thus only an incomplete measurement uncertainty was indicated for these VOS measurements. ...
Measurement of the amount of oil and gas exported from one country to another, or allocated between partners in a license, is made in fiscal metering stations. In 2004 the total export of petroleum from the Norwegian continental shelf was 264 million Sm 3 oil equivalents. For the Norwegian state, taxes, charges and direct ownership related to this export represented a net cash flow of 208.3 billion NOK, or 28 % of the state's total incomes. Fiscal (sales) metering of these large volumes of oil and gas requires highly accurate instruments. A small measurement error can easily translate into a large sum of money for the state and the petroleum industry. In gas metering stations the required uncertainty is typically ±(0.7-1.4) % of the measured value (at 95 % conf. lev.), being regulated and supervised by national authorities (in Norway by the Norwegian Petroleum Directorate, NPD) [1]. Multipath ultrasonic transit time flow meters (USMs) are today extensively used in industry for volumetric flow metering of natural gas, for fiscal measurement, check metering, etc. As an example, Fig. 1 indicates USM based fiscal metering stations for measurement of the Ormen Lange gas, one at Nyhamna in Norway (used for allocation of economic values between the partners), and one in Easington, UK (gas import measurement). In this application, a systematic measurement error of 0.3 % would represent a value of about 150 million NOK per year [2]. As natural gas is normally sold on basis of mass or energy (and not volume), the quantities measured are the volumetric flow rate, pressure (P), temperature (T), density (ρ) and e.g. the gross calorific value (GCV) of the gas. In current fiscal metering stations, gas chromatographs (GC) are widely used for the determination of gas composition and subsequent calculation of gas properties (density, GCV, molecular weight, compressibility, etc.). Alternative methods to measure the density and calorific value in gas metering stations are of interest, for several reasons: • Purchase, use and maintenance of GCs is work demanding and costly, and methods to reduce the number of GCs in fiscal metering stations are in focus. Fig. 1. Schematic illustration of the Ormen Lange / Langeled gas transportation system, with fiscal metering stations at Nyhamna (Norway) and Easington (UK).
... Such processing methods are of interest in relation to a high-precision sound velocity cell for natural gas [5][6][7][8], intended for calibration of the sound velocity measurements in subsea ultrasonic gas flow meters. This sound velocity can potentially be used to calculate the gas energy and mass flow rates in sales and allocation measurement [9]. ...
... This sound velocity can potentially be used to calculate the gas energy and mass flow rates in sales and allocation measurement [9]. Diffraction effects must be accounted for to obtain accurate sound velocity measurements, but existing diffraction correction models, like the piston-type (e.g., [10,11]) and the simplified finite element diffraction correction models [12,8,4], do not provide satisfactory descriptions of such effects [5][6][7][8]. Therefore, a more complete diffraction correction model is needed to reduce and quantify the uncertainty of the sound velocity measurements. ...
... The objective of the present work is to compare and evaluate the performance of the three different processing methods using an example case, relevant for the calculation of the finite-element based diffraction correction for use in a high-precision sound velocity cell for natural gas [5][6][7]. ...
Different signal processing methods are explored to extract individual arrivals from frequency spectra that include interfering direct and multipath arrivals. Specifically, spectrum-of-spectrum (SoS) filtering of the frequency spectrum, cepstrum filtering, and time-signal gating techniques are investigated for an ultrasonic transmit-receive measurement system modeled using a frequency domain transmitter-medium-receiver finite element model. The measurement system consists of two coaxially aligned cylindrical piezoelectric ceramic disks vibrating in air in the frequency range of their first radial resonance. Findings show that all three processing methods are suitable for parts of the frequency range. However, SoS filtering demonstrates the best overall performance for the example case. Cepstrum filtering works well only when the contribution from the direct arrival is significantly stronger than subsequent arrivals. Time-signal gating produces good results only when either the distance between transducers is long enough or the transducers are sufficiently damped to achieve a steady-state signal. A recommendation is made to carefully analyze intermediate steps, or compare different methods, to avoid plausible yet erroneous results.
... Accurate correction for transducer diffraction effects appears to be among the most critical factors in order to realize a high precision sound velocity measurement cell for custody transfer energy measurement of natural gas at elevated pressures [1][2][3][4][5][6]. To achieve 100 -200 ppm relative uncertainty in the sound velocity measurement, there may be need for determining the diffraction correction with high accuracy in the 150 -200 kHz operational frequency range of multipath ultrasonic transit time fiscal gas flow meters [7][8][9]. ...
... However, real transducers do not typically vibrate uniformly, and radiation and reception of sound will also occur at the sides and rear of the transducer, causing interference with the signals propagating directly between the front faces of the transducers. For such cases, an alternative method for calculation of the diffraction correction based on finite element modeling (FEM) was proposed in [14,15] and used e.g. in [2,3,[5][6][7][8][9], referred to as the simplified finite element diffraction correction method (SFDC). ...
... Ultrasonic transit time flow meters are commonly used for fiscal (sales) high-precision flow rate measurement of natural gas [1]. For energy flow rate measurements in subsea applications, a combined use with a high-precision sound velocity cell is of interest for accredited operation [2], [3]. FE modeling of the measurement system is used for control with measurement quantities and transit time corrections, to reduce measurement uncertainty. ...
... By assuming that the transducer front is uniformly insonified by the incoming ultrasound beam, all points of the reflector can be considered as elementary sources with equal face and amplitude. Therefore, each reflector can be regarded as a new plane piston oscillator (Krautkrämer and Krautkrämer, 1983;Leicher et al., 2017b;Norli, 2007;Norli and Lunde, 2006). This is a reasonable assumption, especially in the case of a high-frequency ultrasonic beam and short propagation distance in gases, where the diffraction effects are negligible (Ejakov et al., 2003). ...
In this paper, the concept of a low-cost ultrasonic gas-quality analyzer was studied and experimentally validated. The target gas-quality parameters of propanated biomethane, that is, calorific value and Wobbe index, were predicted by measuring the velocity of sound and the sound attenuation parameter. Both ultrasonic properties were measured with a simple setup of oppositely placed transducers, typical for an ultrasonic gas flow meter operating based on the time-of-flight technique. The velocity of sound and the sound attenuation parameter were measured for the entire range of target gas applications to demonstrate the nonlinear character and deviation from theoretical calculations. The measured data was used to train the regression models based on Gaussian process regression to predict the calorific value and Wobbe index of propanated biomethane.
... Accurate simulation tools for ultrasonic measurement systems are important for design and optimization of ultrasonic measurement instruments, quality assurance in construction of transducers, analysis of measurement data, etc. Applications include e.g. fiscal measurement of oil and gas [1,2], calorific value measurements and gas characterization [3], accurate measurements of sound speed and absorption in gases and liquids [4,5], and non-destructive testing and evaluation. System models in use today include models based on the Mason model (or similar one-dimensional descriptions) for the transmitting and receiving transducers, combined e.g. with uniform piston type of radiation models for the wave propagation in the medium [6][7][8][9][10]; simplified electrical transmission line descriptions [11]; an electroacoustic measurement model [12][13][14], to more advanced FE based descriptions [15,16]. ...
System modeling can be of considerable value for many applications involving ultrasound measurement systems. The objective of the present work is (a) to develop a system model based on finite element (FE) modeling of the transmitting and receiving transducers and sound propagation in the fluid medium, combined with transmission line modeling of the transmitting and receiving electronics and cables, and (b) to compare the system model with measurements. Signal propagation can be modeled in time and frequency domains (signal waveforms and frequency spectra), including description of nearfield diffraction effects. Simulations are compared with measurements for the transmit-receive voltage-to-voltage transfer function of two piezoelectric ceramic disk transducers vibrating in air at 1 atm., over the frequency range of the first two radial modes of the disks.
... Ultrasonic spectroscopy is an invaluable tool used to investigate the mechanical properties of a material [8][9][10]. In particular, it has been used extensively to study the chemical reactions during polymerization of some acrylamide based gels [5,11,12], and the thermal influence on the mechanical properties of a variety of other polymers [5,13,11]. ...
This paper proposes a new method of getting sound velocity by measuring the sound pressure at three positions in a tube. By using LabVIEW software as a platform and building the measurement system, sound velocity at different frequencies in current media is measured. Compared the experimental results with theoretical calculation ones, the correctness of the method discussed in this paper and the reliability of the system are validated.
Open Precision sound velocity cell for natural gas at high pressures. Phase 1-Feasibility study. Extract A feasibility study has been conducted with the objective to work out a proposed method for accurate and traceable measurement of the sound velocity in non-flowing natura! gases, in a precision laboratory cell. The sound velocity of the natura! gas is to be measured in the frequency range between 100 and 200 kHz, preferably at an uncertainty within ±(0.05-0.1) mis (95 % confidence leve!), over the pressure range 0-250 barg, and a temperature range 0-60 °C. A vailable literature on existing methods using sound velocity cells has been reviewed and evaluated with respect to their capabilities and potentitals for use in the above application. From the review, there appears to be no obvious candidate method for the present application, in the sense that none of the reviewed methods can be applied directly for measurement of the sound velocity in pressurized natura! gas, in the relevant frequency band, and to the desired accuracy. Some further development work is required. Two tentative measurement cells have been proposed and described, and especially one of these is considered to be promising for realising a precision sound veiocity cell within the given specifications. The potential applications of such a precision sound velocity cell are several: (1) to analyse the uncertainty of the sound velocity measurement which is made in multipath ultrasonic transit time fiscal flow meters for gas (USM), being taken into use to calculate gas density and potentially energy content, and (2) to establish a more precise sound velocity correction in vibrating element gas densitometers than is used today, to reduce the uncertainty of fiscal mass flowmetering of gas. Such a,cell may also prove to be useful in connection with work on improving the natural gas equation of state, which is an ongoing field of research intemationally. 169 references.
We report a new determination of the Universal Gas Constant R: (8. 314 471 plus or minus 0. 000 014) J multiplied by (times) mol** minus **1K** minus **1. The uncertainty in the new value is 1. 7 ppm (standard error), a factor of 5 smaller than the uncertainty in the best previous value. The gas constant was determined from measurements of the speed of sound in argon as a function of pressure at the temperature of the triple point of water. The speed of sound was measured with a spherical resonator whose volume was determined by weighing the mercury required to fill it at the temperature of the triple point. The molar mass of the argon was determined by comparing the speed of sound in it to the speed of sound in a standard sample of argon of accurately known chemical and isotopic composition.
For a circular plane piston of radius a, producing an ultrasonic beam with propagation constant k (or 2ir/X), an expression is derived for the velocity potential or the acoustic pressure, averaged with respect to magnitude and phase over a “measurement circle” equal in area to the piston and centered in the beam. The expression should be highly accurate for ka^ 100, at distances z from the source governed by (z/a)^ ka. It agrees well with results computed, in another way, by Huntington, Emslie, and Hughes. The assumption that relatively near the source there is a collimated beam of plane waves is shown to be not very accurate; the averaged pressure falls off monotonically over all distances considered. The velocity potential at the rim of the “measurement circle” is also computed, and compared with the plane wave assumption.
Calculations and tables are given for the exact diffraction corrections to the results of ultrasound phase velocity measurement for circular transducers of equal radius. Simple formulae have been obtained for the diffraction corrections within the approximations of plane and spherical waves.
This paper describes a precise numerical calculation of the specific heat ratio and speed of sound in air as a function of temperature, pressure, humidity, and CO2 concentration. The above parameters are calculated utilizing classical thermodynamic relationships and a real gas equation of state over the temperature range 0-degrees-C-30-degrees-C. The shortcomings of previous determinations are also discussed. For both parameters, the coefficients of an interpolating equation are given, which are suitable for use in applications requiring high precision. The overall uncertainty in the specific heat ratio is estimated to be less than 320 ppm and the uncertainty in the speed of sound is similarly estimated to be less than 300 ppm.
A new method has been developed for the accurate measurement of the velocity of compressional waves in solid specimens. This is based on the cancellation of a traveling wave train, which has undergone reflection at the ends of the specimen, by a second wave train launched from the same transducer. A description is given of the experimental system employed.
A correction must be made for the phase shift which occurs when the ultrasonic signal is reflected at the interface between specimen and transducer. A theoretical study of the effects of the transducer and coupling film shows that the correction is a function of the resonant frequency of the transducer and of the ratio of acoustic impedance of the transducer to that of the specimen.
The application of the correction enables the velocity of propagation to be determined to within 1 in 104.