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Measurement of density using oscillation-type density meters. Calibration, traceability and Uncertainties
Conference Paper · June 2009
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Andreia Furtado Elsa Batista Instituto Português da Qualidade Instituto Português da Qualidade
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The user has requested enhancement of the downloaded file. MEASUREMENT OF DENSITY USING OSCILLATION-TYPE DENSITY METERS CALIBRATION, TRACEABILITY AND UNCERTAINTIES
A. Furtado, E. Batista, I. Spohr, E. Filipe Instituto Português da Qualidade (IPQ) Rua António Gião, 2 – Caparica – Portugal [email protected]
quality control of fuels and additives; in the chemical and Résumé nuclear, to determine the concentration of acids, bases and other solutions and to determine radioactive substances concentration; in the food industry, cosmetics, etc. La masse volumique d'un fluide peut être déterminé en utilisant plusieurs instruments de mesure. Récemment, les This magnitude can be determined using several densimètres à oscillations ont montré une grande measuring instruments, such as pycnometers, hydrometers polyvalence, ils sont utilisés en différentes branches de and oscillation-type density meters, and also using the l'industrie. Le Laboratoire des Propriétés des Liquides method of hydrostatic weighing. Recently the oscillation- (LPL) de l'Institut Portugais pour la Qualité (IPQ) réalise type density meters have shown great versatility, and are l'étalonnage de ces instruments par rapport à un étalon de being used in various branches of industry. The advantages densimètres à oscillations, dans l’intervalle de mesure de 3 of using these instruments are its response time, its use la masse volumique de (500 à 2 000) kg/m . La traçabilité simplicity and the small volume of the needed sample. des mesures est assurée par des solutions certifiées du PTB et de la DKD. La nécessité d'assurer la traçabilité métrologique à un système de détermination absolue de la Measurement of liquids density masse volumique des liquides a conduit à des évolutions récentes dans ce domaine, qui seront décrites dans ce From Archimedes to Hans Stabinger document. Il sera également décrit le modèle mathématique et le bilan d’'incertitude de l'étalonnage de Formally assigned to Archimedes, but invented by Hipatia densimètres à oscillations. of Alexandria (370-415 DC), the hydrometers are the oldest, simple, highly effective and widely used tools for Abstract measuring the density with different levels of accuracy.
The density of a fluid can be determined using several The method for hydrometers calibration, based on measuring instruments. Recently the oscillation-type hydrostatic weighing, was introduced by Cuckow [1] in density meters have shown great versatility, being used in 1949. This method allows hydrometers of any range to be various branches of industry. The Laboratory of Properties calibrated at any point of its scale through the of Liquids (LPL) of the Portuguese Institute for Quality measurement of the force of buoyancy in the air and when (IPQ) performs the calibration of these instruments by immersed in the reference liquid (see Figure 1A). This is comparison with a standard density meter, in the 3 the most accurate method and is used in most National measuring interval of density from (500 to 2 000) kg/m . Metrology Institutes, including the IPQ [2]. The The metrological traceability is given by Certified participation in the EURAMET 702 Project, gave LPL the Reference Materials (CRMs) of PTB and DKD. The need recognition of its Calibration and Measurement Capability to ensure traceability to a system of absolute determination (CMC) in the calibration of hydrometers by the Cuckow of the density of liquids has led to recent developments in Method’s, using n-nonane at 20 °C, in a density measuring 3 this area which will be described in this paper. It will be interval [3] from (750 to 1 000) kg/m , with an expanded Frequency oscillator also described the mathematical model and uncertainty uncertainty of 0,1 kg/m3 for an expansion coefficient, budget of the calibration of the oscillation-type density k = 2. meters.
Introduction The density is defined as the property of a body, given by the ratio of its mass to its volume (kg/m3). The fluid density is a major key in the control of most industrial processes, because it allows not only, a better management of the process but also the accurate determination of the quantity and quality of the product. The measurement of A B the density is used in drinks industry, to control the alcohol content in binary mixtures or the sugar content in soft drinks and fruit juices; in the pharmaceutical industry, to Figure 1. A - System for hydrometers calibration; determine the specific gravity of medicinal preparations; in B - System for measuring the density of the oil industry to determine the API gravity and for the liquids by hydrostatic weighing. In 1967, the company Anton Paar GmbH presented the Where is the sample density, the cell volume, m the first digital density meter for liquids and gases. It was the mass cell and C the spring constant. Applying the square first instrument to use the principle of the U shaped 2 2 4 v 4 m vibrating tube, of Stabinger Hans and Hans Leopold for of Eq. 1, and substituting G and H we C C the determination of the density. These first obtain: oscillation-type density meters were subject to errors induced by the viscosity in most of the samples. These ( 2 H) 3 (2) errors were usually higher than 0,7 kg/m in instruments G with a resolution of 0,1 kg/m3. In 1998, Hans Stabinger developed a density meter (Paar DMA 5000) with a new During the oscillation of the U tube, the sample shows the measurement cell which applied the viscosity correction of effect of damping of the oscillation. This damping is a the sample, thereby avoiding the systematic errors of the function of the viscosity sample. The sample viscosity will others instruments. also have the effect of apparently slightly move the oscillation nodes, thus increasing the apparent volume of the cell. When these two effects are combined, the error k , Oscillation-type density meters in kg/m3, is of the order of k 0,05 , where is the Principle of operation viscosity in mPa·s.
The working principle of an oscillation-type density meter The measurement cell oscillates at several frequencies in is based on the law of harmonic oscillation, in which a U two modes. This allows the damping due to the sample to tube is completely filled with the sample to be analyzed, be measured and properly corrected. When the standard is and subjected to an electromagnetic force. The calibrated, the density is a function of the oscillation measurement of the frequency and duration of vibration of period, and the damping. the tube filled with the sample, allows the determination of the density value of the sample. This measuring principle The internal software of the instrument includes the is based on the Mass-Spring Model. assumption that:
The measuring cell consists of an oscillator formed by an 2 2 4 (3) hallow U-shaped borosilicate glass tube that comprises A (1 Ddamping E damping ) B C about 0,7 ml of the sample. This tube has double walls and the space between them is filled with a gas with high where A, B, C and D are coefficients determined in the coefficient of thermal conductivity. In that space is also instrument calibration using two substances of known placed a platinum resistance thermometer that allows the densities, typically air and water. Studies made in several temperature measurement of the fluid during the density instruments of the same type using a wide range of CRMs, measurement. The remaining instrumentation consists of a and water suggested that the Eq. 3 with its interaction system of electronic excitement and electrical components between the period and damping is unnecessarily complex 3 that provide a signal transmission of the period for the [4]. For samples of density between (690 and 1 620) kg/m processor unit, free of interferences (see Figure 2). and viscosity above 600 mPa·s an equation of the form A B 2 C damping is more appropriate. For liquids in the same density range, but with viscosities Evaluation Display below 30 mPa·s, the Eq. 4 describes better the cell behaviour.
Coil 2 C (4) Amplifier A B damping
Magnet Calibration Frequency oscillator Method and Metrological Traceability Glass tube
The calibrations of oscillation-type density meters held by LPL are performed at 20 ºC, through a comparative Figure 2. Measurement cell of an oscillation-type density method, using aqueous solutions in a density measuring meters. interval from (500 to 2 000) kg/m3. It follows a procedure
which has as a reference document the ISO 15212-1:1998 The U tube oscillates at its fundamental frequency, which [5]. The density of the prepared solutions is measured with is a function of the system mass. If we assume that the the standard density meter of LPL (Anton Paar DMA5000) sample volume inside the cell is constant, it can be seen and the density meter of the client. The density that the oscillation frequency is therefore a function of the measurement of the liquid samples in both density meters sample density. The oscillation period , is given by: are held almost simultaneously, thus ensuring that the solution is in the same conditions of homogeneity. The v m 2 (1) Certification of density of liquid samples is carried out C using an internal procedure based on the same ISO.
The results of calibration, certification and the uncertainty rectangular distribution. Table 1 describes the uncertainty budget, which will be further presented, are made in an sources mentioned. Excel sheet previously validated for that purpose. The results obtained in the calibration are presented in a Table 1- Uncertainty contributions in kg/m3 for the Certificate of Calibration, that also describes the combined standard uncertainty of oscillation-type density characteristics of the calibrated instrument, conditions of meters calibration and density certification of liquid operation, errors and expanded uncertainty associated with samples. each value of density tested. The results of the certification Uncertainty Uncertainty Uncertainty of density of liquid samples are presented in a Certificate, Distribution Contributions Components Category describing the characteristics of the sample, conditions of (kg/m3) the operation and an associated uncertainty. Standard density meter -2 ucalibration B Normal 2,5×10 -2 The metrological traceability [3] of density measurements uCRMs B Normal 2,5×10 -5 is achieved through calibration of the oscillation-type uresolution B Rectangular 2,9×10 density meter with density standard samples of CRMs urepeatability A Normal variable from PTB and DKD. The traceability of temperature utemperature B Rectangular negligible measurements of the sample is assured by calibration of a urepeatability A Normal variable platinum resistance thermometer in the Temperature utemperature B Rectangular negligible Laboratory of IPQ. Client density meter urepeatability A Normal variable -4 Uncertainty Budget uresolution B Rectangular 2,9×10 The uncertainties were calculated according to the GUM [6]. The uncertainty associated with the calibration of an oscillation-type density meter is calculated combining two Concluding Remarks sources of uncertainty of measurement: one of the client The oscillating tube density meter area of the LPL is density meter (uclient density meter) and the other of the standard growing in terms of the number of clients that asks for density meter (ustandard density meter). The uncertainty density certification of liquid samples and calibration of associated with the certification of density of liquid density meters. The LPL main goal is to complete the samples is only related with the uncertainty of chain of the metrological traceability of liquid density measurement of standard density meter (see Figure 3). measurement. Since 2005, LPL has been working to
uclient density meter improve a system that allows the determination of the liquids density by hydrostatic weighing, using as a density urepeatability standard, a silicon sphere, which mass and density are knew and certified (see Figure 1.B), allowing the decrease uresolution ucalibration of uncertainty in density certification. Up to now, the LPL ucertification participated in two EURAMET projects, which are still u repeatability ucalibration on-going. We are looking forward to open new calibration and certification areas, in particularly, in viscosity and utemperature uCRMs u u repeatability temperature surface tension, as well as to develop new CRMs for those ustandard density meter uresolution two properties.
Figure 3. Cause and effect diagram with the uncertainty References contributions for the combined standard uncertainty of oscillation-type density meters calibration, by comparative method and [1] Cuckow, F.W., “A new method of high accuracy for certification of liquid samples density. the calibration of reference standard hydrometers”, J. Chem. Ind., Vol. 68, pp. 44-9, 1949. The component of the standard uncertainty associated with [2] Ferreira, M.C. e Dias, J.M., “The role of experimental the repeatability of the measurements (type A) is obtained design in the hydrometer field”, XVIII Imeko World by the standard deviation of the density measurements Congress, Brazil, 2006. [3] ISO/IEC GUIDE 99:2007, International vocabulary average (urepeatability). The other uncertainty components are evaluated by the type B method, including the uncertainty of metrology - Basic and general concepts and associated terms (VIM). related with the resolution (uresolution) of both density meters, as a rectangular distribution. Usually, the density [4] Stabinger, H., "Density Measurement using modern meters calibrated at IPQ have a resolution of 1×10-1 kg/m3, oscillating transducers", South Yorkshire Trading a resolution 100 times higher than the resolution of the Standards Unit, Sheffield, 1994 standard density meter. The main contribution to the [5] “Oscillation type density meters – Laboratory measurement uncertainty of the density meter standard is instruments. ISO 15212-1, 1998. [6] “Guide to the Expression of uncertainty in the uncertainty of the CRMs (uCRMs) used for its calibration. Finally, the uncertainty component due to the Measurement.” BIPM et al - 1.ª ed. Genève: International sample temperature inside the cell (u ), has a Organization for Standardization, 1995. temperature
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