Densimeter calibration method versus temperature and pressure

Lagourette, B.; Boned, Christian; Saint-Guirons, H.; Xans, P.; Zhou, Honggang

doi:10.1088/0957-0233/3/8/002

Cited by 234 publications

(197 citation statements)

References 11 publications

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“…The estimated uncertainty of the measured temperature is ±0.01 K between (293.15 and 353.15 K) (Anton Paar MKT50 thermometer) while the estimated uncertainty of the measured pressure is ±0.015 MPa (Presents Precise Gold Plus pressure transmitter); as a consequence, the uncertainty on the density measurement is estimated to be ±0.5 kg m −3 (i.e., around 0.05% for density close to that of water). This uncertainty is similar to that reported in several other studies [14][15][16][17].…”

Section: High-pressure Density Measurementsupporting

confidence: 91%

Density Measurements of Waste Cooking Oil Biodiesel and Diesel Blends Over Extended Pressure and Temperature Ranges

2018

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Density and compressibility are primordial parameters for the optimization of diesel engine operation. With this objective, these properties were reported for waste cooking oil biodiesel and its blends (5% and 10% by volume) mixed with diesel. The density measurements were performed over expanded ranges of pressure (0.1 to 140 MPa) and temperature (293.15 to 353.15 K) compatible with engine applications. The isothermal compressibility was estimated within the same experimental range by density differentiation. The Fatty Acid Methyl Esters (FAMEs) profile of the biodiesel was determined using a Gas Chromatography-Mass Spectrometry (GC-MS) technique. The storage stability of the biodiesel was assessed in terms of the reproducibility of the measured properties. The transferability of this biodiesel fuel was discussed on the basis of the standards specifications that support their use in fuel engines. Additionally, this original set of data represents meaningful information to develop new approaches or to evaluate the predictive capability of models previously developed.

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Section: High-pressure Density Measurementsupporting

confidence: 91%

Density Measurements of Waste Cooking Oil Biodiesel and Diesel Blends Over Extended Pressure and Temperature Ranges

2018

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“…The spring constant was assumed to be independent of pressure and its temperature dependence was represented by a fourth-order polynomial, while the tube volume was assumed to vary linearly with pressure and as a cubic function of temperature. The assumptions made regarding pressure dependence of the parameters were consistent with the second method described by Lagourette et al 8 and Sousa et al 9 although many more parameters were used to describe empirically the temperature variation of the apparatus parameters given the much wider range of operating temperature.…”

Section: Ideally the Calibration Measurements Used To Determine A(pmentioning

confidence: 92%

“…None of these, however, have been tested over the wide range of conditions considered in this work, namely pressures to 140 MPa and temperatures from 273 to 473 K. In 1992 Lagourette et al 8 and Sousa et al 9 independently described methods for calibrating VTDs supplied by Anton Paar, including the model DMA 512 which is a stainless steel VTD operable at pressures to 40 MPa and temperatures to 423 K. These calibration methods involved the determination of the evacuated tube's resonance period as a function of temperature and the use of an assumption regarding the pressure dependence of A or B, which was informed by a physical model of the vibrating tube. In one method 8 , only B was assumed to vary (linearly) with pressure whereas in the second method 8,9 A and B were assumed to have the same pressure coefficient so that the ratio A/B was independent of pressure. Lagourette et al 8 found the first method resulted in a calibration that represented the reference fluid densities slightly better, although the second method has a more physical basis (as will be seen below).…”

Section: Ideally the Calibration Measurements Used To Determine A(pmentioning

confidence: 99%

“…In one method 8 , only B was assumed to vary (linearly) with pressure whereas in the second method 8,9 A and B were assumed to have the same pressure coefficient so that the ratio A/B was independent of pressure. Lagourette et al 8 found the first method resulted in a calibration that represented the reference fluid densities slightly better, although the second method has a more physical basis (as will be seen below).…”

Section: Ideally the Calibration Measurements Used To Determine A(pmentioning

confidence: 99%

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Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K

May

Tay

Nania

et al. 2014

Review of Scientific Instruments

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Vibrating tube densimeters are well-established tools for measuring fluid densities precisely at elevated temperatures and pressures. However, the conventional method of calibrating them utilises a model in which the apparatus parameters are represented as polynomials of temperature and pressure that contain a variable number of terms. Here a robust, physically-based model is presented and demonstrated for six different instruments at temperatures from (273 to 473) K, pressures from (0 to 140) MPa and densities from (0 to 1050) kg m -3 . The model's physical basis ensures that only seven apparatus parameters are required to relate the measured resonant period to fluid mass density with an average r.m.s. deviation of ±0.23 kg m -3 across all six densimeters. Estimates for each of the apparatus parameters were made based on the geometry and material properties of the vibrating tubes, and these estimates were consistent with the parameter values determined by calibration with reference fluids. Three of the apparatus parameters describe the temperature dependence of the resonant period: for the six vibrating tubes tested, the relative standard deviations of these parameters were all within the range of values estimated from the thermoelastic properties of the Hastelloy tubes. Two distinct parameters are required to describe the pressure dependence of the vibrating tube's volume and effective spring constant, both of which are estimable from equations describing the elastic deformation of thick-walled tubes. The extensive calibrations conducted demonstrate that, for these densimeters, the variations with pressure of the tube's spring constant and its volume have a ratio that is neither 0 nor 1, as has been assumed previously. The model's physical basis allows vibrating tube densimeters to be calibrated accurately using fewer reference fluid measurements than required by the conventional method. Furthermore, use of the physically-based model reduces the uncertainty of measurements made at densities, temperatures or pressures beyond the range of the calibration.1

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“…For a vibrating tube density sensor (Lagourette et al, 1992), the relationship between the density and the resonance frequency is…”

mentioning

confidence: 99%

Bayesian Information for Sensors

Eves

Wang

Walker

2014

Quality & Reliability Eng

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An engineering company 1 manufacturing high precision sensors had accumulated huge historical databases of information on a type of sensors which had been tested. The aim of the company was not to use this historical data to improve estimation of future individual sensor parameters, but rather to use it to reduce the number of measurements needed per sensor, guaranteeing a required level of accuracy. In the paper we show how this can be done, using Bayesian ideas, and introduce the novel theory for linear regression models which determines how the reduction in individual sensor measurements can be achieved.Specifically, for estimating parameters of closely related sensors, an estimate can be thought of as comprising a global component, i.e. the mean of all the sensors, and a local component, which is a shift from the mean. The historical data can, in a Bayesian framework, provide the global component and hence all that is needed from an individual sensor is the local component. In non-Bayesian estimation methods, both components are required and hence many measurements are needed. On the other hand, with Bayesian methods, only the local fit is needed and hence fewer measurements per sensor are required. We provide the supporting theory and demonstrate on a real-life application with real data.

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Densimeter calibration method versus temperature and pressure

Cited by 234 publications

References 11 publications

Density Measurements of Waste Cooking Oil Biodiesel and Diesel Blends Over Extended Pressure and Temperature Ranges

Density Measurements of Waste Cooking Oil Biodiesel and Diesel Blends Over Extended Pressure and Temperature Ranges

Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K

Bayesian Information for Sensors

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