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Density of standard seawater by vibrating tube densimeter: Analysis of the method and results
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Density of standard seawater by vibrating tube densimeter: Analysis of the method and results R. Romeo *, P.A. Giuliano Albo, S. Lago Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, Turin, 10135, Italy
A R T I C L E I N F O
A B S T R A C T
Keywords: Seawater Density Vibrating tube densimeter Salinity
Seawater density has a great importance in oceanography, since it drives the ocean currents that drift oxygen, heat, plankton and pollutants. If the density is measured with high accuracy, it can be also used for salinity determination. In this work, the density of standard seawater was measured at different absolute salinities from (10.044–38.178) g kg 1, in the temperature range of (278.15–313.15) K at atmospheric pressure. The mea surements were carried out by means of a commercial vibrating tube densimeter, following the substitution method (alternating samples of seawater and water) and under conditions typical of the most oceanographic laboratories capabilities. Besides, an accurate analysis of the uncertainty of density was performed, obtaining a relative expanded uncertainty of 0.003% (k ¼ 2). Measurements were compared with the density values pro vided by the international reference equation of state: the Thermodynamic Equation of SeaWater-2010, TEOS-10.
1. Introduction The knowledge of seawater density is a matter of concern since ocean currents, such as the thermohaline circulation, are driven by density differences due to temperature or salt variations (UNESCO, 1981; Wright et al., 2011). For this reason, salinity is a crucial quantity handy to describe ocean physical properties and oceanic dynamic variations. As discussed in Le Menn et al. (2019), the definition of absolute salinity may be based on various physical quantities, thus considering as salinity measurands conductivity, speed of sound, refractive index, and density. In the past, the thermodynamic properties of seawater, i.e., Equation of state of Seawater (UNESCO, 1981), were described in terms of Prac tical Salinity, SP , which is essentially a measure of the conductivity of seawater. SP is defined in terms of the ratio K15 of the electrical con ductivity of a seawater sample at 288.15 K and atmospheric pressure, to that of a potassium chloride solution of mass fraction 0.0324356, at the same temperature and pressure. Since 2010, the thermodynamic of seawater is described by the Thermodynamic Equation of Seawater 2010 (IOC et al., 2010), in terms of absolute salinity, SA , defined as the mass fraction of dissolved material per kilogram of seawater. Since seawater properties are influenced by the mass of dissolved constituents, SA is preferred to SP because it depends on electrical conductivity only, which is not enough to detect composition anomalies (Pawlowicz et al.,
2011; Feistel, 2015). In order to use density for SA determinations comparable to values of salinity obtained by conductivity measurements, an accuracy of2⋅10 3 kg m 3 in density measurement is mandatory (Schmidt et al., 2016). Thus, as claimed by Schmidt et al. (2018), density measurements can be used to obtain the salinity of seawater by means of a density-salinity relation: the more accurate density measurements are, the more accu rate the salinity determination is. Furthermore, they determined the relation linking the density to the salinity, the temperature and the pressure for standard seawater. That paper states also that an increase of salinity from 0 g kg 1 to 35 g kg 1 leads to a density increase of only 3%. Therefore, density has to be measured with a relative uncertainty of 10 6 to detect salinity variations at the level of 10 3 g kg 1. Besides, to ensure traceability to the International System of unit (SI) is essential to monitor long term salinity trends, since they are clima tologically relevant (Feistel, 2015). According to Seitz et al. (2011); Feistel (2018), density is the most promising candidate to be used for the metrological traceability of standard seawater to the SI, since density of standard seawater can be measured with the necessary accuracy and its measurement is SI-traceable. Considering the described framework, this work aims to measure the density of standard seawater by means of a vibrating tube densimeter following a well established procedure that can be adopted with typical oceanographic laboratories equipment, and to evaluate performances
* Corresponding author. E-mail address: [email protected] (R. Romeo). https://doi.org/10.1016/j.dsr.2019.103157 Received 25 March 2019; Received in revised form 28 October 2019; Accepted 1 November 2019 Available online 7 November 2019 0967-0637/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: R. Romeo, Deep–Sea Research I, https://doi.org/10.1016/j.dsr.2019.103157
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(by analyzing the measurement uncertainty) of the capabilities commonly available in oceanographic laboratories.
cell. These two parameters are defined as follows
2. Materials and methods In order to measure density, several methods can be used based on different physical principles (Goodwin et al., 2003). Experimental dif ficulties may arise in many measurement methodologies, where the influence of pressure, temperature and composition should be consid ered. Nowadays, the most widespread methods used to carry out mea surements of seawater density at atmospheric pressure are the vibrating tube densimeter and the hydrostatic weighing. Indeed the literature shows that the most accurate measurements were carried out with these techniques, which allow measurements with an uncertainty in the order of few parts per million (ppm). As reported in Le Menn et al. (2019), also the pycnometric method has to be mentioned as a possible technique to measure seawater density. This method has the advantage to avoid phenomena that affect the sample composition, but the uncertainty is currently higher than in the other techniques.
Vibrating tube densimeters are widely used for density measure ments of several different fluids, with applications in research and in dustry since many years (Picker et al., 1974). The most attractive characteristics of this technique are the high precision, the operation simplicity and the low volume of sample requested. This is the most widespread technique exploited to measure the density of seawater both in metrological and oceanographic laboratories. Firstly, Poisson and Gadhoumi (1993) used a vibrating tube densimeter for seawater measurements at atmospheric pressure (the uncertainty is not stated). Millero and Huang (2009) measured the density of seawater between (273.15 and 363.15) K at atmospheric pressure and in a wide range of absolute salinity, from about (4–70) g kg 1. As reported in Wolf (2008), vibrating tube densimeter allows to carry out density measurements with a relative uncertainty of 10 6 at atmospheric pressure. Indeed, Schmidt et al. (2016) measured standard seawater density at atmospheric pressure and at temperatures from (278.15–308.15) K with a declared relative uncertainty of 2 ppm. Recently Bud�eus (2018) carried out density measurements of ocean water samples from different areas (Antarctica, Arctic and North Atlantic waters), by means of a vibrating tube densimeter and with a relative uncertainty of 5 ppm. It is worth pointing out that such accuracy of few ppm can be reached only under best working conditions. Following a different procedure, e.g., without automatic filling system, leads to lower accuracy, as demonstrated in this work. On the other hand, at higher pressure (up to 140 MPa) this instru ment can measure seawater density with an uncertainty in the order of 10 4. Safarov et al. (2009), Safarov et al. (2012) and Safarov et al. (2013) carried out density measurements of standard seawater up to 140 MPa, covering an absolute salinity range between (2 and 55) g kg 1 and at temperatures up to 468.15 K, with a reproducibility of 0.03%. The working principle of the vibrating tube densimeter is based on the measure of the mechanical resonant frequency of a metal or glass Utube, filled with the examined fluid. The oscillation period, corre sponding to the value of a resonant frequency, is directly correlated to the density of the sample, which depends mainly on the working tem perature and pressure (Romeo et al., 2017). The tube, isolated in a thermostated cell, is filled with the sample of interest and vibrates perpendicular to its plane by means of the piezoelectric transducer. The density is obtained with the following empirical relation, by measuring the period, τ, instead of frequency: BðT; pÞ;
KðT; pÞ 4π2 VðT; pÞ
(2)
B¼
M0 ; VðT; pÞ
(3)
where K is the tube stiffness, V is the inner volume of the tube and M0 is the mass of the evacuated tube. The instrument parameters are deter mined by measuring the period in two reference fluids of well-known density. To simplify the calibration procedure, the period is usually measured in vacuum, and, e.g., in water. However, different methods can be used to calibrate the densimeter. Commonly, A and B are determined using a polynomial function of temperature and pressure. May et al. (2014) reviewed the main methods and proposed a new calibration model based on the physical parameters of the system. In this approach the parameters are derived from the geometry and material properties of the apparatus, and fewer mea surements of the reference fluids than conventional methods are requested. The performances of this calibration method are comparable with those obtained by measuring the oscillation period in a reference fluid and when the cell is evacuated. However, it shows that the ap proximations made in Eq. (1) are acceptable.
2.1. Vibrating tube densimeter
ρðT; pÞ ¼ AðT; pÞτ2
A¼
2.2. Hydrostatic weighing For many fluids, especially in liquid phase, the method to measure density with the lowest uncertainty is the hydrostatic weighing. The working method is based on the Archimedes’ buoyancy principle: the upward buoyant force exerted on a body, the sinker, immersed in a fluid is equal to the weight of the fluid that the body displaces. The sinker is usually a sphere or a cylinder, made of a chemically inactive solid ma terial with long term stability (glass-ceramic or metal), of known mass and volume. The fluid density, ρ, is expressed by
ρ¼
m�s
ms Vs
;
(4)
where ms is the mass of the sinker weighted in vacuum, m�s is the “apparent” mass of the sinker immersed in the liquid sample and Vs is the volume of the sinker. With this method, the density is traceable to the basequantities mass and length, through the apparent mass and the volume of the sinker used, so that calibration fluids are not required and for this reason this method is considered a primary method in metrology. For density measurements, obtained in conditions different from those of the sinker certificate, volume corrections are needed. If the requested uncertainty is in the order of a few parts per million, the isothermal compressibility and the thermal expansion coefficients of the sinker material have to be known with the necessary accuracy. A com bination of the Achimedes’ principle with magnetic suspension allows to reach wide-ranging measurements, in particular high pressure mea surements. A magnetic suspension coupling transmits the weight of the sinker to the analytical balance, and separates the fluid, which may be at extremes temperature and pressure, from the balance at ambient con ditions (Goodwin et al., 2003; Kuramoto et al., 2004; McLinden and €sch-Will, 2007). Nevertheless, the magnetic suspension brings out Lo additional sources of uncertainty, e.g., the repeatability of the floating position and the force transmission error, so that these types of densimeters are affected by uncertainties higher than those obtained without magnetic suspension. While the best hydrostatic weighing at ambient pressure is charac terized by expanded relative uncertainty of about 5 ppm (Fehlauer and Wolf, 2006), most of the hydrostatic balances with magnetic suspension have a relative uncertainty around (15 or 20) ppm, with the exception of
(1)
where A and B are parameters depending on the characteristics of the 2
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Kayukawa et al. (2012). The different value is due to additional sources of uncertainty introduced by the magnetic suspension, e.g., the repeat ability of the floating position and the force transmission error (Le Menn et al., 2019). If density is measured at higher pressure, uncertainty can only grow. Besides, these levels of accuracy can be obtained only with chemically stable fluids. For other chemically active fluids, such as seawater, hydrostatic weighing can be used to measure density both at atmospheric and higher pressure, but with a higher uncertainty, around 15–100 ppm (Goodwin et al., 2003). Although the hydrostatic weighing is a primary method capable to measure density with high accuracy, this technique required sophisti cate apparatus and tools that many laboratories are unlikely equipped with. For this reason hydrostatic weighing is usually not exploited for routinely measurements and, generally, it is not available in oceano graphic facilities.
values of humidity were usually around 30–40%. The samples of water were prepared by means of a GFL Water Still for double distillation 2102, just before starting the measurement, so that further degas ification was not necessary. The bottles of seawater were softly shacked, but not degassed in order to avoid changes in the composition. Bidis tilled water and seawater were measured alternatively, carefully cleaning and drying the vibrating tube before manually changing the liquid. Before starting the measurement, the tube was cleaned by the DSA 5000 M air pump, filled with acetone/ethanol and then dried both using the air pump and by increasing the temperature at about 323 K. Each filling (both for bidistilled water and seawater) was made by means of glass syringes, taking care to avoid any bubble formation in the used syringe. Before each measurement, the syringe was cleaned with acetone and dried with nitrogen. After the densimeter was loaded, the in strument’s camera was used to check that no bubbles formed even into the capillary and then the measurement was performed. On the other hand, when bubbles formed, the capillary had to be emptied, cleaned and dried before filling up again. After a seawater sample was measured the capillary was evacuated and cleaned by flowing pure water inside it. Then the tube was dried by using the dry air pump and setting the temperature around 323 K. Usually before starting a new measurement cycle the water and air adjustment at 293.15 K was repeated. The temperature was measured by means of the internal thermom eter of the DSA 5000 M (manufacturer resolution of �0.001 K), which was calibrated by comparison with a reference platinum resistance thermometer. Therefore, standard seawater samples density was obtained by means of Eq. (5). As stated by Wolf (2008), the substitution method minimizes systematic errors affecting the uncertainty, such as non-linearity, and long-term and temperature drift of the measuring apparatus. As reference fluid ρref;meas , bidistilled water was measured and as reference values, ρref , IAPWS-95 formulation by Wagner and Pruss (2002) was used. Each measurement was repeated 5 times, and the average of the values was taken into account.
2.3. Seawater density measurements through vibrating tube densimeter As previously cited, vibrating tube densimeter seems to be a suitable technique to carry out density measurements of seawater. Indeed, nowadays, the most accurate measurements of seawater density at at mospheric pressure are those carried out by Schmidt et al. (2016), at temperatures between (278.15 and 308.15) K and salinity up to 35 g kg 1. The measurements were performed by a vibrating tube densimeter using the substitution method, which allows to determine seawater density, ρ, by the following equation:
ρðT; SA Þ ¼ ρref ðTÞ
(5)
ρref;meas ðTÞ þ ρmeas ðT; SA Þ
where ρref is the reference density of water given by Wagner and Pruss (2002), ρref;meas is the density of bidistilled water measured by the vibrating tube, while ρmeas is the seawater density measured with the same vibrating tube. The densities by Schmidt et al. (2016) are measured with a relative uncertainty of 2⋅10 6 . This condition seems to be achievable exclusively under hard experimental arrangement: e.g., Schmidt et al. (2016) used an automatic system that needs 20 h per sample. The purpose of this work is to measure seawater density at different salinity by means of a commercial vibrating tube densimeter, at atmo spheric pressure and as a function of temperature, and also to evaluate the instrument’s performances under routinely conditions, since nowa days this is the device used worldwide in the laboratories of oceano graphic institutes. The vibrating tube used is a DSA 5000 M provided by Anton Paar. Since the vibrating tube is sensitive to the angle of the instrument, the horizontality of the DSA 5000 M was verified by means of a bubble level. Samples of IAPSO Standard Seawater delivered by OSIL are used. The practical salinity, SP , of the samples is certified by OSIL (see Table 1 for details). The values of SP were converted in SA by the formula reported in McDougall et al. (2012), with an uncertainty of 0.007 g kg 1. As claimed in Le Menn (2011), the uncertainty of the practical salinity obtained by conductivity measurements is0.003, and this value could be associated to the SP declared by OSIL. The vibrating tube densimeter was firstly calibrated with air and freshly bidistilled water at 293.15 K. Ambient pressure and humidity were monitored by means of a Mini Datalogger HD206-2 and a Paroscientific Mod. 745, respectively. The
3. Results Density of seawater was measured at temperatures between (278.15–313.15) K with step of 5 K and at ambient pressure condition. The experimental data are listed in Table 2. In Fig. 1, the obtained values of seawater density are shown as a function of temperature. Four curves are reported corresponding to the four measured samples of different salinity. All the curves show the same behavior as a function of temperature. By roughly analyzing the data of Table 2, it is possible to observe that the increment of density with ab solute salinity is linear. 3.1. Uncertainty From a metrological point of view, seawater density is obtained by considering it as a function of the reference density, the density mea surements obtained by the vibrating tube (for water and seawater), the measured temperature, and the absolute salinity: � (6) ρ ¼ ρ ρref ; ρref;meas ; ρmeas ; T; SA Consequently, according to the Guide to the expression of uncertainty in measurements (BIPM et al., 2008), by applying the uncertainty prop agation formula, the relative uncertainty of seawater density is esti mated as follows: ffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� � uðρÞ 1 ∂ρ 2 2 ∂ρ 2 2 2 2 2 u ρref þ d þ σ ðρÞ þ ¼ u ðTÞ þ u ðSA Þ (7) ∂T ∂SA ρ ρ
Table 1 Properties of the samples of standard seawater (OSIL) used in this work: batch, practical salinity and corresponding absolute salinity. Sample
Batch
SP
SA / g kg
1 2 3 4
38H14 P160 30L18 10L16
37.999 34.993 30.000 9.997
38.178 35.158 30.141 10.044
1
where uðρref Þ is the uncertainty of the reference density of water, pro vided by the IAPWS-95 formulation (Wagner and Pruss, 2002), d is the 3
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Table 2 Seawater density ρ(relative uncertainty T/ K
ρ / kg m
UðρÞ
ρ
3
SA ¼ 10.044 g kg 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
¼ 30 ppm, with k ¼ 2) at temperature T and at different absolute salinity SA .
1
SA ¼ 30.141 g kg
1007.946 1007.540 1006.815 1005.830 1004.605 1003.124 1001.466 999.605
1023.749 1023.092 1022.160 1020.990 1019.599 1018.009 1016.237 1014.293
1
SA ¼ 35.158 g kg 1027.678 1026.955 1025.971 1024.758 1023.330 1021.716 1019.930 1017.964
1
SA ¼ 38.178 g kg
1
1030.090 1029.330 1028.318 1027.078 1025.632 1024.002 1022.192 1020.218
magnitude higher than the other sources of uncertainty). This was evaluated for each measurement cycle, but finally only the worst value was considered as repeatability contribution to the uncertainty for all the samples. The repeatability term was estimated as recommended by BIPM et al. (2008), taking into account real working conditions, e.g., presence of small bubbles not detected by the camera, cleaning, hys teresis, evaporation or stratification, and pressure variations. The value related to the repeatability is due to the manual performance of the experimental measurements. Using an automatic procedure might improve the repeatability, but would obviously increase the working time considerably. 3.2. Comparison between experimental results and equation of state (TEOS-10) The densities obtained through the DSA 5000 M, and shown in Table 2, were compared with the current reference equation of state for seawater: the Thermodynamic Equation of SeaWater-2010, or TEOS-10 (IOC et al., 2010). Fig. 2 reports the deviations of the experimental re sults from TEOS-10 (represented by the zero line). The deviations are all within 50 ppm, so considering the experimental combined uncertainty calculated by Eq. (7) (namely 30 ppm), most of the measurements are in agreement with the equation of state. However, generally the experi mental values are systematically higher than TEOS-10. Focus on salinity of SA ¼ 35.158 g kg 1, there is good agreement between the equation of state and the measurements: the deviations are lower than�10 ppm. Thus, measurements performed for the sample standard salinity are the
Fig. 1. Experimental density as a function of temperature at different salinity: (□), SA ¼ 38.178 g kg 1; (�), SA ¼ 35.158 g kg 1; (△), SA ¼ 30.141 g kg 1; (▾), SA ¼ 10.044 g kg 1.
resolution of the vibrating tube densimeter, and σ ðρÞ is the repeatability of the measurements; those two the contributions to the uncertainties of both ρref;meas and ρmeas . The temperature uncertainty isuðTÞ ¼ 0:01 K (estimated by the sensor calibration, the resolution and stability of the instrument, and the reading repeatability). Since SA was not measured by the authors of this work, its uncertainty, uðSA Þ, was assumed starting from the value estimated by Le Menn (2011), combined with the value reported in McDougall et al. (2012). The sensitivity coefficients of temperature and salinity,
∂ρ ∂T
and
∂ρ ∂SA
respectively, were evaluated from
the experimental data. The relative uncertainty in the measurements of density is calculated using Eq. (7), with a coverage factor k ¼ 2. The resulting uncertainty is 0.003% with a confidence level of 95%. Table 3 provides the sources of uncertainty and the relative uncertainties contributing to the overall uncertainty of seawater density. It is clear that the major contribution to the uncertainty is given by the measurement repeatability (an order of Table 3 Density uncertainty budget. Uncertainty source
Relative magnitude %
reference water density temperature resolution repeatability salinity
0.0001 0.0005 0.0001 0.0020 0.0005
Relative combined uncertainty (k ¼ 2)
0.003
Fig. 2. Deviations of experimental densities from the fundamental equation of state TEOS-10 as a function of temperature at different salinity: (□), SA ¼ 38.178 g kg 1; (�), SA ¼ 35.158 g kg 1; (△), SA ¼ 30.141 g kg 1; (▾), SA ¼ 10.044 g kg 1. 4
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best represented by TEOS-10. On the other hand the more salinity differs from standard salinity the more the experimental results deviate from TEOS-10. The experimental results were compared with the data of Schmidt et al. (2018) given in the supplementary material. However, the de viations are around 50 ppm and the densities of Schmidt et al. (2018) are lower than the ones of this work.
Table 4 Comparison between seawater densities measured by the vibrating tube UðρÞ densimeter, ρ at SA ¼ 35.158 g kg 1 (relative uncertainty ¼ 30 ppm, with
ρ
k ¼ 2), and by the hydrostatic weighing, ρhw at SA ¼ 35.159 g kg Uðρhw Þ uncertainty ¼ 8 ppm, with k ¼ 2).
1
(relative
ρhw
3.3. Preliminary measurements with hydrostatic weighing At the laboratories of Istituto Nazionale di Ricerca Metrologica (INRIM), also a hydrostatic weighing without magnetic suspension was used to carried out preliminary measurements of seawater density by Giuliano Albo et al. (2018). Density was obtained for seawater samples of SA ¼ 35:159 g kg 1 at 288.15 K and 293.15 K with a relative uncer tainty of 8 ppm. In Table 4, the values of seawater density, at the standard salinity, are reported, along with the relative deviations. Considering both the relative uncertainties obtained for density measured by the DSA 5000 M and by the hydrostatic weighing, the measurements are in very good agreement since the deviations are less than 2 ppm. At 288.15 K the density values differ of about 1 ppm (1.2 ppm), while at 293.15 K less than 1 ppm (0.2 ppm). Measurements with hydrostatic weighing are still in progress at INRIM, planned to be carried out in a wider range of temperature and using samples of other salinities. An overall comparison between results obtained with the two methods is going to be done, useful also to evaluate TEOS-10 behavior.
T/K
ρ / kg m
288.15 293.15
1025.971 1024.758
3
ρhw / kg m 1025.972 1024.758
3
ρ
106 ⋅ 1 <1
ρhw ρhw
Since the measurements with the hydrostatic weighing are still in progress, further comparisons will be performed with the new results, to evaluate differences between the two experimental methods and the behavior of TEOS-10. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OILM, 2008. Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurements, JMGM 100: 2008 GUM 1995 with Minor Corrections. Bud�eus, G. Th, 2018. Potential bias in TEOS10 density of sea water samples. Deep-Sea Res. Part I Oceanogr. Res. Pap. 134, 41–47. Fehlauer, H., Wolf, H., 2006. Density reference liquids certified by the PhysikalischTechnische Buundesanstalt. Meas. Sci. Technol. 17, 2588–2592. Feistel, R., 2015. Salinity and relative humidity: climatological relevance and metrological needs. Acta IMEKO 4, 57–61. Feistel, R., 2018. Thermodynamic properties of seawater, ice and humid air: TEOS-10, before and beyond. Ocean Sci. 14, 471–502. Giuliano Albo, P.A., Lago, S., Romeo, R., Malengo, A., 2018. Density measurements of IAPSO seawater by single sinker hydrostatic balance. In: 17th International Conference on the Properties of Water and Steam, Prague, Czech Republic. Goodwin, A.R.H., Marsh, W.A., Wakeham, W.A., 2003. Measurement of the Thermodynamic Properties of Single Phases, Experimental Thermodynamics, vol. VI. Elsevier. IOC, SCOR, IAPSO, 2010. The international thermodynamic equation of seawater – 2010: calculation and use of thermodynamic properties. In: Intergovernmental Oceanographic Commission, Manuals and Guides N. 56, UNESCO (English), 196. Kayukawa, Y., Kano, Y., Fujii, K., Sato, H., 2012. Absolute density measurements by dual sinker magnetic levitation densimeter. Metrologia 49, 513–521. Kuramoto, N., Fujii, K., Waseda, A., 2004. Accurate density measurements of reference liquids by a magnetic suspension balance. Metrologia 41, S84–S94. Le Menn, M., 2011. About uncertainties in practical salinity calculations. Ocean Sci. 7, 651–659. Le Menn, M., Giuliano Albo, P.A., Lago, S., Romeo, R., Sparasci, F., 2019. The absolute salinity of seawater and its measurands. Metrologia 56, 015005. May, E.F., Tay, W.J., Nania, M., Aleji, A., Al-Ghafri, S., 2014. Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K. Rev. Sci. Instrum. 85, 095111. McLinden, M.O., L€ osch-Will, C., 2007. Apparatus for wide-ranging, high-accuracy fluid (p,ρ,T)measurements based on a compact twosinker densimeter. J. Chem. Thermodyn. 39, 507–530. McDougall, T.J., Jackett, D.R., Millero, F.J., Pawlowicz, R., Baker, P.M., 2012. A global algorithm for estimating Absolute Salinity. Ocean Sci. 8, 1123–1134. Millero, F.J., Huang, F., 2009. The density of seawater as a function of salinity (5 to 70 g kg 1) and temperature (273.15 to 363.15 K). Ocean Sci. 5, 91–100. Pawlowicz, R., Wright, D.G., Millero, F.J., 2011. The effects of biogeochemical processes on oceanic conductivity/salinity/density relationships and the characterization of real seawater. Ocean Sci. 7, 363–387. Picker, P., Tremblay, E., Jolicoeur, C., 1974. A high-precision digital readout flow densimeter for liquids. J. Solut. Chem. 3, 377–384. Poisson, A., Gadhoumi, M.H., 1993. An extension of the practical salinity scale 1978 and the equation of state 1980 to high salinities. Deep Sea Res. 40, 1689–1698. Romeo, R., Giuliano Albo, P.A., Lago, S., Brown, J.S., 2017. Experimental liquid densities of cis-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(Z)) and trans-1-chloro-3,3,3trifluoropropene (R1233zd(E)). Int. J. Refrig. 79, 176–182. Safarov, J., Berndt, S., Millero, F., Feistel, R., Heintz, A., Hassel, E., 2012. (p,ρ,T) properties of seawater: extensions to high salinities. Deep-Sea Res. I 65, 146–156. Safarov, J., Berndt, S., Millero, F.J., Feistel, R., Heintz, A., Hassel, E.P., 2013. (p,ρ,T) Properties of seawater at brackish salinities: extensions to high temperatures and pressures. Deep-Sea Res. I 78, 95–101.
4. Conclusion In this work, the density of seawater was measured. Samples of standard seawater of different absolute salinity, SA ¼ (10.044, 30.141, 35.158 and 38.178) g kg 1, provided by OSIL were studied, and the densities were obtained at eight temperatures: from (278.15–313.15) K every 5 K at atmospheric pressure. The measurements were carried out by means of a commercial vibrating tube densimeter (Anton Paar DSA 5000 M), using the substitution method. Seawater and pure water was measured alternatively, in order to correct the measured values by the comparison between experimental pure water density and reference values by Wagner and Pruss (2002). The substitution method allowed to avoid systematic errors of the instrument and drifting effects. The relative uncertainty of seawater density was estimated by considering all the sources of uncertainty and resulted to be 0.003%, with a coverage factor k ¼ 2. With the followed experimental procedure, the main contribution to the uncertainty is due to the repeatability. The perfor mances of the vibrating tube could be evaluated under routinely work ing conditions. Indeed, the uncertainty value obtained in this work is one order of magnitude higher than the one obtained, e.g., by Schmidt et al. (2016), who followed a more sophisticated procedure (e.g., auto matic system for filling). Therefore, with routinely working conditions, vibrating tubes can measure density with a relative uncertainty around 10 5. The experimental densities were compared with the data given by the dedicated equation of state for seawater TEOS-10 (IOC et al., 2010). All the deviations are in agreement with TEOS-10 within 50 ppm. However, experimental densities seem to be systematically higher than TEOS-10. Besides this comparison shows that measurements performed for the sample with absolute salinity of 35.158 g kg 1 are those in better agreement with TEOS-10 since the deviations are within � 10 ppm. This suggests that further investigation of seawater density is needed, espe cially for salinity different from 35.158 g kg 1. The measurements were also compared with preliminary results carried out by Giuliano Albo et al. (2018), by means of a hydrostatic balance for seawater of standard salinity at two temperatures: 283.15 K and 293.15 K. This first com parison showed good agreement (with deviations better than 2 ppm), between measurements performed with the two independent methods. 5
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Safarov, J., Millero, F., Feistel, R., Heintz, A., Hassel, E., 2009. Thermodynamic properties of standard seawater: extensions to high temperatures and pressure. Ocean Sci. 5, 235–246. Schmidt, H., Seitz, S., Hassel, E., Wolf, H., 2018. The density-salinity relation of standard seawater. Ocean Sci. 14, 15–40. Schmidt, H., Wolf, H., Hassel, E., 2016. A method to measure the density of seawater accurately to the level of 10 6. Metrologia 53, 772–786. Seitz, S., Feistel, R., Wright, D.G., Weinreben, S., Spitzer, P., De Bi�evre, P., 2011. Metrological traceability of oceanographic salinity measurement results. Ocean Sci. 7, 45–62.
UNESCO, 1981. The practical salinity scale 1978 and the international equation of state of seawater 1980. In: UNESCO Technical Papers in Marine Science, vol. 36. UNESCO, Paris. Wagner, W., Pruss, A., 2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535. Wright, D.G., Pawlowicz, R., McDougall, T.J., Feistel, R., Marion, G.M., 2011. Absolute salinity, “density salinity” and the reference-composition salinity scale: present and future use in the seawater standard TEOS-10. Ocean Sci. 7, 1–26. Wolf, H., 2008. Determination of water density: limitations at the uncertainty level of 1�10 6. Accred Qual. Assur. 13, 587–591.
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Deep-Sea Research Part I journal homepage: http://www.elsevier.com/locate/dsri
Density of standard seawater by vibrating tube densimeter: Analysis of the method and results R. Romeo *, P.A. Giuliano Albo, S. Lago Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, Turin, 10135, Italy
A R T I C L E I N F O
A B S T R A C T
Keywords: Seawater Density Vibrating tube densimeter Salinity
Seawater density has a great importance in oceanography, since it drives the ocean currents that drift oxygen, heat, plankton and pollutants. If the density is measured with high accuracy, it can be also used for salinity determination. In this work, the density of standard seawater was measured at different absolute salinities from (10.044–38.178) g kg 1, in the temperature range of (278.15–313.15) K at atmospheric pressure. The mea surements were carried out by means of a commercial vibrating tube densimeter, following the substitution method (alternating samples of seawater and water) and under conditions typical of the most oceanographic laboratories capabilities. Besides, an accurate analysis of the uncertainty of density was performed, obtaining a relative expanded uncertainty of 0.003% (k ¼ 2). Measurements were compared with the density values pro vided by the international reference equation of state: the Thermodynamic Equation of SeaWater-2010, TEOS-10.
1. Introduction The knowledge of seawater density is a matter of concern since ocean currents, such as the thermohaline circulation, are driven by density differences due to temperature or salt variations (UNESCO, 1981; Wright et al., 2011). For this reason, salinity is a crucial quantity handy to describe ocean physical properties and oceanic dynamic variations. As discussed in Le Menn et al. (2019), the definition of absolute salinity may be based on various physical quantities, thus considering as salinity measurands conductivity, speed of sound, refractive index, and density. In the past, the thermodynamic properties of seawater, i.e., Equation of state of Seawater (UNESCO, 1981), were described in terms of Prac tical Salinity, SP , which is essentially a measure of the conductivity of seawater. SP is defined in terms of the ratio K15 of the electrical con ductivity of a seawater sample at 288.15 K and atmospheric pressure, to that of a potassium chloride solution of mass fraction 0.0324356, at the same temperature and pressure. Since 2010, the thermodynamic of seawater is described by the Thermodynamic Equation of Seawater 2010 (IOC et al., 2010), in terms of absolute salinity, SA , defined as the mass fraction of dissolved material per kilogram of seawater. Since seawater properties are influenced by the mass of dissolved constituents, SA is preferred to SP because it depends on electrical conductivity only, which is not enough to detect composition anomalies (Pawlowicz et al.,
2011; Feistel, 2015). In order to use density for SA determinations comparable to values of salinity obtained by conductivity measurements, an accuracy of2⋅10 3 kg m 3 in density measurement is mandatory (Schmidt et al., 2016). Thus, as claimed by Schmidt et al. (2018), density measurements can be used to obtain the salinity of seawater by means of a density-salinity relation: the more accurate density measurements are, the more accu rate the salinity determination is. Furthermore, they determined the relation linking the density to the salinity, the temperature and the pressure for standard seawater. That paper states also that an increase of salinity from 0 g kg 1 to 35 g kg 1 leads to a density increase of only 3%. Therefore, density has to be measured with a relative uncertainty of 10 6 to detect salinity variations at the level of 10 3 g kg 1. Besides, to ensure traceability to the International System of unit (SI) is essential to monitor long term salinity trends, since they are clima tologically relevant (Feistel, 2015). According to Seitz et al. (2011); Feistel (2018), density is the most promising candidate to be used for the metrological traceability of standard seawater to the SI, since density of standard seawater can be measured with the necessary accuracy and its measurement is SI-traceable. Considering the described framework, this work aims to measure the density of standard seawater by means of a vibrating tube densimeter following a well established procedure that can be adopted with typical oceanographic laboratories equipment, and to evaluate performances
* Corresponding author. E-mail address: [email protected] (R. Romeo). https://doi.org/10.1016/j.dsr.2019.103157 Received 25 March 2019; Received in revised form 28 October 2019; Accepted 1 November 2019 Available online 7 November 2019 0967-0637/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: R. Romeo, Deep–Sea Research I, https://doi.org/10.1016/j.dsr.2019.103157
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(by analyzing the measurement uncertainty) of the capabilities commonly available in oceanographic laboratories.
cell. These two parameters are defined as follows
2. Materials and methods In order to measure density, several methods can be used based on different physical principles (Goodwin et al., 2003). Experimental dif ficulties may arise in many measurement methodologies, where the influence of pressure, temperature and composition should be consid ered. Nowadays, the most widespread methods used to carry out mea surements of seawater density at atmospheric pressure are the vibrating tube densimeter and the hydrostatic weighing. Indeed the literature shows that the most accurate measurements were carried out with these techniques, which allow measurements with an uncertainty in the order of few parts per million (ppm). As reported in Le Menn et al. (2019), also the pycnometric method has to be mentioned as a possible technique to measure seawater density. This method has the advantage to avoid phenomena that affect the sample composition, but the uncertainty is currently higher than in the other techniques.
Vibrating tube densimeters are widely used for density measure ments of several different fluids, with applications in research and in dustry since many years (Picker et al., 1974). The most attractive characteristics of this technique are the high precision, the operation simplicity and the low volume of sample requested. This is the most widespread technique exploited to measure the density of seawater both in metrological and oceanographic laboratories. Firstly, Poisson and Gadhoumi (1993) used a vibrating tube densimeter for seawater measurements at atmospheric pressure (the uncertainty is not stated). Millero and Huang (2009) measured the density of seawater between (273.15 and 363.15) K at atmospheric pressure and in a wide range of absolute salinity, from about (4–70) g kg 1. As reported in Wolf (2008), vibrating tube densimeter allows to carry out density measurements with a relative uncertainty of 10 6 at atmospheric pressure. Indeed, Schmidt et al. (2016) measured standard seawater density at atmospheric pressure and at temperatures from (278.15–308.15) K with a declared relative uncertainty of 2 ppm. Recently Bud�eus (2018) carried out density measurements of ocean water samples from different areas (Antarctica, Arctic and North Atlantic waters), by means of a vibrating tube densimeter and with a relative uncertainty of 5 ppm. It is worth pointing out that such accuracy of few ppm can be reached only under best working conditions. Following a different procedure, e.g., without automatic filling system, leads to lower accuracy, as demonstrated in this work. On the other hand, at higher pressure (up to 140 MPa) this instru ment can measure seawater density with an uncertainty in the order of 10 4. Safarov et al. (2009), Safarov et al. (2012) and Safarov et al. (2013) carried out density measurements of standard seawater up to 140 MPa, covering an absolute salinity range between (2 and 55) g kg 1 and at temperatures up to 468.15 K, with a reproducibility of 0.03%. The working principle of the vibrating tube densimeter is based on the measure of the mechanical resonant frequency of a metal or glass Utube, filled with the examined fluid. The oscillation period, corre sponding to the value of a resonant frequency, is directly correlated to the density of the sample, which depends mainly on the working tem perature and pressure (Romeo et al., 2017). The tube, isolated in a thermostated cell, is filled with the sample of interest and vibrates perpendicular to its plane by means of the piezoelectric transducer. The density is obtained with the following empirical relation, by measuring the period, τ, instead of frequency: BðT; pÞ;
KðT; pÞ 4π2 VðT; pÞ
(2)
B¼
M0 ; VðT; pÞ
(3)
where K is the tube stiffness, V is the inner volume of the tube and M0 is the mass of the evacuated tube. The instrument parameters are deter mined by measuring the period in two reference fluids of well-known density. To simplify the calibration procedure, the period is usually measured in vacuum, and, e.g., in water. However, different methods can be used to calibrate the densimeter. Commonly, A and B are determined using a polynomial function of temperature and pressure. May et al. (2014) reviewed the main methods and proposed a new calibration model based on the physical parameters of the system. In this approach the parameters are derived from the geometry and material properties of the apparatus, and fewer mea surements of the reference fluids than conventional methods are requested. The performances of this calibration method are comparable with those obtained by measuring the oscillation period in a reference fluid and when the cell is evacuated. However, it shows that the ap proximations made in Eq. (1) are acceptable.
2.1. Vibrating tube densimeter
ρðT; pÞ ¼ AðT; pÞτ2
A¼
2.2. Hydrostatic weighing For many fluids, especially in liquid phase, the method to measure density with the lowest uncertainty is the hydrostatic weighing. The working method is based on the Archimedes’ buoyancy principle: the upward buoyant force exerted on a body, the sinker, immersed in a fluid is equal to the weight of the fluid that the body displaces. The sinker is usually a sphere or a cylinder, made of a chemically inactive solid ma terial with long term stability (glass-ceramic or metal), of known mass and volume. The fluid density, ρ, is expressed by
ρ¼
m�s
ms Vs
;
(4)
where ms is the mass of the sinker weighted in vacuum, m�s is the “apparent” mass of the sinker immersed in the liquid sample and Vs is the volume of the sinker. With this method, the density is traceable to the basequantities mass and length, through the apparent mass and the volume of the sinker used, so that calibration fluids are not required and for this reason this method is considered a primary method in metrology. For density measurements, obtained in conditions different from those of the sinker certificate, volume corrections are needed. If the requested uncertainty is in the order of a few parts per million, the isothermal compressibility and the thermal expansion coefficients of the sinker material have to be known with the necessary accuracy. A com bination of the Achimedes’ principle with magnetic suspension allows to reach wide-ranging measurements, in particular high pressure mea surements. A magnetic suspension coupling transmits the weight of the sinker to the analytical balance, and separates the fluid, which may be at extremes temperature and pressure, from the balance at ambient con ditions (Goodwin et al., 2003; Kuramoto et al., 2004; McLinden and €sch-Will, 2007). Nevertheless, the magnetic suspension brings out Lo additional sources of uncertainty, e.g., the repeatability of the floating position and the force transmission error, so that these types of densimeters are affected by uncertainties higher than those obtained without magnetic suspension. While the best hydrostatic weighing at ambient pressure is charac terized by expanded relative uncertainty of about 5 ppm (Fehlauer and Wolf, 2006), most of the hydrostatic balances with magnetic suspension have a relative uncertainty around (15 or 20) ppm, with the exception of
(1)
where A and B are parameters depending on the characteristics of the 2
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Kayukawa et al. (2012). The different value is due to additional sources of uncertainty introduced by the magnetic suspension, e.g., the repeat ability of the floating position and the force transmission error (Le Menn et al., 2019). If density is measured at higher pressure, uncertainty can only grow. Besides, these levels of accuracy can be obtained only with chemically stable fluids. For other chemically active fluids, such as seawater, hydrostatic weighing can be used to measure density both at atmospheric and higher pressure, but with a higher uncertainty, around 15–100 ppm (Goodwin et al., 2003). Although the hydrostatic weighing is a primary method capable to measure density with high accuracy, this technique required sophisti cate apparatus and tools that many laboratories are unlikely equipped with. For this reason hydrostatic weighing is usually not exploited for routinely measurements and, generally, it is not available in oceano graphic facilities.
values of humidity were usually around 30–40%. The samples of water were prepared by means of a GFL Water Still for double distillation 2102, just before starting the measurement, so that further degas ification was not necessary. The bottles of seawater were softly shacked, but not degassed in order to avoid changes in the composition. Bidis tilled water and seawater were measured alternatively, carefully cleaning and drying the vibrating tube before manually changing the liquid. Before starting the measurement, the tube was cleaned by the DSA 5000 M air pump, filled with acetone/ethanol and then dried both using the air pump and by increasing the temperature at about 323 K. Each filling (both for bidistilled water and seawater) was made by means of glass syringes, taking care to avoid any bubble formation in the used syringe. Before each measurement, the syringe was cleaned with acetone and dried with nitrogen. After the densimeter was loaded, the in strument’s camera was used to check that no bubbles formed even into the capillary and then the measurement was performed. On the other hand, when bubbles formed, the capillary had to be emptied, cleaned and dried before filling up again. After a seawater sample was measured the capillary was evacuated and cleaned by flowing pure water inside it. Then the tube was dried by using the dry air pump and setting the temperature around 323 K. Usually before starting a new measurement cycle the water and air adjustment at 293.15 K was repeated. The temperature was measured by means of the internal thermom eter of the DSA 5000 M (manufacturer resolution of �0.001 K), which was calibrated by comparison with a reference platinum resistance thermometer. Therefore, standard seawater samples density was obtained by means of Eq. (5). As stated by Wolf (2008), the substitution method minimizes systematic errors affecting the uncertainty, such as non-linearity, and long-term and temperature drift of the measuring apparatus. As reference fluid ρref;meas , bidistilled water was measured and as reference values, ρref , IAPWS-95 formulation by Wagner and Pruss (2002) was used. Each measurement was repeated 5 times, and the average of the values was taken into account.
2.3. Seawater density measurements through vibrating tube densimeter As previously cited, vibrating tube densimeter seems to be a suitable technique to carry out density measurements of seawater. Indeed, nowadays, the most accurate measurements of seawater density at at mospheric pressure are those carried out by Schmidt et al. (2016), at temperatures between (278.15 and 308.15) K and salinity up to 35 g kg 1. The measurements were performed by a vibrating tube densimeter using the substitution method, which allows to determine seawater density, ρ, by the following equation:
ρðT; SA Þ ¼ ρref ðTÞ
(5)
ρref;meas ðTÞ þ ρmeas ðT; SA Þ
where ρref is the reference density of water given by Wagner and Pruss (2002), ρref;meas is the density of bidistilled water measured by the vibrating tube, while ρmeas is the seawater density measured with the same vibrating tube. The densities by Schmidt et al. (2016) are measured with a relative uncertainty of 2⋅10 6 . This condition seems to be achievable exclusively under hard experimental arrangement: e.g., Schmidt et al. (2016) used an automatic system that needs 20 h per sample. The purpose of this work is to measure seawater density at different salinity by means of a commercial vibrating tube densimeter, at atmo spheric pressure and as a function of temperature, and also to evaluate the instrument’s performances under routinely conditions, since nowa days this is the device used worldwide in the laboratories of oceano graphic institutes. The vibrating tube used is a DSA 5000 M provided by Anton Paar. Since the vibrating tube is sensitive to the angle of the instrument, the horizontality of the DSA 5000 M was verified by means of a bubble level. Samples of IAPSO Standard Seawater delivered by OSIL are used. The practical salinity, SP , of the samples is certified by OSIL (see Table 1 for details). The values of SP were converted in SA by the formula reported in McDougall et al. (2012), with an uncertainty of 0.007 g kg 1. As claimed in Le Menn (2011), the uncertainty of the practical salinity obtained by conductivity measurements is0.003, and this value could be associated to the SP declared by OSIL. The vibrating tube densimeter was firstly calibrated with air and freshly bidistilled water at 293.15 K. Ambient pressure and humidity were monitored by means of a Mini Datalogger HD206-2 and a Paroscientific Mod. 745, respectively. The
3. Results Density of seawater was measured at temperatures between (278.15–313.15) K with step of 5 K and at ambient pressure condition. The experimental data are listed in Table 2. In Fig. 1, the obtained values of seawater density are shown as a function of temperature. Four curves are reported corresponding to the four measured samples of different salinity. All the curves show the same behavior as a function of temperature. By roughly analyzing the data of Table 2, it is possible to observe that the increment of density with ab solute salinity is linear. 3.1. Uncertainty From a metrological point of view, seawater density is obtained by considering it as a function of the reference density, the density mea surements obtained by the vibrating tube (for water and seawater), the measured temperature, and the absolute salinity: � (6) ρ ¼ ρ ρref ; ρref;meas ; ρmeas ; T; SA Consequently, according to the Guide to the expression of uncertainty in measurements (BIPM et al., 2008), by applying the uncertainty prop agation formula, the relative uncertainty of seawater density is esti mated as follows: ffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� � uðρÞ 1 ∂ρ 2 2 ∂ρ 2 2 2 2 2 u ρref þ d þ σ ðρÞ þ ¼ u ðTÞ þ u ðSA Þ (7) ∂T ∂SA ρ ρ
Table 1 Properties of the samples of standard seawater (OSIL) used in this work: batch, practical salinity and corresponding absolute salinity. Sample
Batch
SP
SA / g kg
1 2 3 4
38H14 P160 30L18 10L16
37.999 34.993 30.000 9.997
38.178 35.158 30.141 10.044
1
where uðρref Þ is the uncertainty of the reference density of water, pro vided by the IAPWS-95 formulation (Wagner and Pruss, 2002), d is the 3
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Table 2 Seawater density ρ(relative uncertainty T/ K
ρ / kg m
UðρÞ
ρ
3
SA ¼ 10.044 g kg 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
¼ 30 ppm, with k ¼ 2) at temperature T and at different absolute salinity SA .
1
SA ¼ 30.141 g kg
1007.946 1007.540 1006.815 1005.830 1004.605 1003.124 1001.466 999.605
1023.749 1023.092 1022.160 1020.990 1019.599 1018.009 1016.237 1014.293
1
SA ¼ 35.158 g kg 1027.678 1026.955 1025.971 1024.758 1023.330 1021.716 1019.930 1017.964
1
SA ¼ 38.178 g kg
1
1030.090 1029.330 1028.318 1027.078 1025.632 1024.002 1022.192 1020.218
magnitude higher than the other sources of uncertainty). This was evaluated for each measurement cycle, but finally only the worst value was considered as repeatability contribution to the uncertainty for all the samples. The repeatability term was estimated as recommended by BIPM et al. (2008), taking into account real working conditions, e.g., presence of small bubbles not detected by the camera, cleaning, hys teresis, evaporation or stratification, and pressure variations. The value related to the repeatability is due to the manual performance of the experimental measurements. Using an automatic procedure might improve the repeatability, but would obviously increase the working time considerably. 3.2. Comparison between experimental results and equation of state (TEOS-10) The densities obtained through the DSA 5000 M, and shown in Table 2, were compared with the current reference equation of state for seawater: the Thermodynamic Equation of SeaWater-2010, or TEOS-10 (IOC et al., 2010). Fig. 2 reports the deviations of the experimental re sults from TEOS-10 (represented by the zero line). The deviations are all within 50 ppm, so considering the experimental combined uncertainty calculated by Eq. (7) (namely 30 ppm), most of the measurements are in agreement with the equation of state. However, generally the experi mental values are systematically higher than TEOS-10. Focus on salinity of SA ¼ 35.158 g kg 1, there is good agreement between the equation of state and the measurements: the deviations are lower than�10 ppm. Thus, measurements performed for the sample standard salinity are the
Fig. 1. Experimental density as a function of temperature at different salinity: (□), SA ¼ 38.178 g kg 1; (�), SA ¼ 35.158 g kg 1; (△), SA ¼ 30.141 g kg 1; (▾), SA ¼ 10.044 g kg 1.
resolution of the vibrating tube densimeter, and σ ðρÞ is the repeatability of the measurements; those two the contributions to the uncertainties of both ρref;meas and ρmeas . The temperature uncertainty isuðTÞ ¼ 0:01 K (estimated by the sensor calibration, the resolution and stability of the instrument, and the reading repeatability). Since SA was not measured by the authors of this work, its uncertainty, uðSA Þ, was assumed starting from the value estimated by Le Menn (2011), combined with the value reported in McDougall et al. (2012). The sensitivity coefficients of temperature and salinity,
∂ρ ∂T
and
∂ρ ∂SA
respectively, were evaluated from
the experimental data. The relative uncertainty in the measurements of density is calculated using Eq. (7), with a coverage factor k ¼ 2. The resulting uncertainty is 0.003% with a confidence level of 95%. Table 3 provides the sources of uncertainty and the relative uncertainties contributing to the overall uncertainty of seawater density. It is clear that the major contribution to the uncertainty is given by the measurement repeatability (an order of Table 3 Density uncertainty budget. Uncertainty source
Relative magnitude %
reference water density temperature resolution repeatability salinity
0.0001 0.0005 0.0001 0.0020 0.0005
Relative combined uncertainty (k ¼ 2)
0.003
Fig. 2. Deviations of experimental densities from the fundamental equation of state TEOS-10 as a function of temperature at different salinity: (□), SA ¼ 38.178 g kg 1; (�), SA ¼ 35.158 g kg 1; (△), SA ¼ 30.141 g kg 1; (▾), SA ¼ 10.044 g kg 1. 4
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best represented by TEOS-10. On the other hand the more salinity differs from standard salinity the more the experimental results deviate from TEOS-10. The experimental results were compared with the data of Schmidt et al. (2018) given in the supplementary material. However, the de viations are around 50 ppm and the densities of Schmidt et al. (2018) are lower than the ones of this work.
Table 4 Comparison between seawater densities measured by the vibrating tube UðρÞ densimeter, ρ at SA ¼ 35.158 g kg 1 (relative uncertainty ¼ 30 ppm, with
ρ
k ¼ 2), and by the hydrostatic weighing, ρhw at SA ¼ 35.159 g kg Uðρhw Þ uncertainty ¼ 8 ppm, with k ¼ 2).
1
(relative
ρhw
3.3. Preliminary measurements with hydrostatic weighing At the laboratories of Istituto Nazionale di Ricerca Metrologica (INRIM), also a hydrostatic weighing without magnetic suspension was used to carried out preliminary measurements of seawater density by Giuliano Albo et al. (2018). Density was obtained for seawater samples of SA ¼ 35:159 g kg 1 at 288.15 K and 293.15 K with a relative uncer tainty of 8 ppm. In Table 4, the values of seawater density, at the standard salinity, are reported, along with the relative deviations. Considering both the relative uncertainties obtained for density measured by the DSA 5000 M and by the hydrostatic weighing, the measurements are in very good agreement since the deviations are less than 2 ppm. At 288.15 K the density values differ of about 1 ppm (1.2 ppm), while at 293.15 K less than 1 ppm (0.2 ppm). Measurements with hydrostatic weighing are still in progress at INRIM, planned to be carried out in a wider range of temperature and using samples of other salinities. An overall comparison between results obtained with the two methods is going to be done, useful also to evaluate TEOS-10 behavior.
T/K
ρ / kg m
288.15 293.15
1025.971 1024.758
3
ρhw / kg m 1025.972 1024.758
3
ρ
106 ⋅ 1 <1
ρhw ρhw
Since the measurements with the hydrostatic weighing are still in progress, further comparisons will be performed with the new results, to evaluate differences between the two experimental methods and the behavior of TEOS-10. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OILM, 2008. Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurements, JMGM 100: 2008 GUM 1995 with Minor Corrections. Bud�eus, G. Th, 2018. Potential bias in TEOS10 density of sea water samples. Deep-Sea Res. Part I Oceanogr. Res. Pap. 134, 41–47. Fehlauer, H., Wolf, H., 2006. Density reference liquids certified by the PhysikalischTechnische Buundesanstalt. Meas. Sci. Technol. 17, 2588–2592. Feistel, R., 2015. Salinity and relative humidity: climatological relevance and metrological needs. Acta IMEKO 4, 57–61. Feistel, R., 2018. Thermodynamic properties of seawater, ice and humid air: TEOS-10, before and beyond. Ocean Sci. 14, 471–502. Giuliano Albo, P.A., Lago, S., Romeo, R., Malengo, A., 2018. Density measurements of IAPSO seawater by single sinker hydrostatic balance. In: 17th International Conference on the Properties of Water and Steam, Prague, Czech Republic. Goodwin, A.R.H., Marsh, W.A., Wakeham, W.A., 2003. Measurement of the Thermodynamic Properties of Single Phases, Experimental Thermodynamics, vol. VI. Elsevier. IOC, SCOR, IAPSO, 2010. The international thermodynamic equation of seawater – 2010: calculation and use of thermodynamic properties. In: Intergovernmental Oceanographic Commission, Manuals and Guides N. 56, UNESCO (English), 196. Kayukawa, Y., Kano, Y., Fujii, K., Sato, H., 2012. Absolute density measurements by dual sinker magnetic levitation densimeter. Metrologia 49, 513–521. Kuramoto, N., Fujii, K., Waseda, A., 2004. Accurate density measurements of reference liquids by a magnetic suspension balance. Metrologia 41, S84–S94. Le Menn, M., 2011. About uncertainties in practical salinity calculations. Ocean Sci. 7, 651–659. Le Menn, M., Giuliano Albo, P.A., Lago, S., Romeo, R., Sparasci, F., 2019. The absolute salinity of seawater and its measurands. Metrologia 56, 015005. May, E.F., Tay, W.J., Nania, M., Aleji, A., Al-Ghafri, S., 2014. Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K. Rev. Sci. Instrum. 85, 095111. McLinden, M.O., L€ osch-Will, C., 2007. Apparatus for wide-ranging, high-accuracy fluid (p,ρ,T)measurements based on a compact twosinker densimeter. J. Chem. Thermodyn. 39, 507–530. McDougall, T.J., Jackett, D.R., Millero, F.J., Pawlowicz, R., Baker, P.M., 2012. A global algorithm for estimating Absolute Salinity. Ocean Sci. 8, 1123–1134. Millero, F.J., Huang, F., 2009. The density of seawater as a function of salinity (5 to 70 g kg 1) and temperature (273.15 to 363.15 K). Ocean Sci. 5, 91–100. Pawlowicz, R., Wright, D.G., Millero, F.J., 2011. The effects of biogeochemical processes on oceanic conductivity/salinity/density relationships and the characterization of real seawater. Ocean Sci. 7, 363–387. Picker, P., Tremblay, E., Jolicoeur, C., 1974. A high-precision digital readout flow densimeter for liquids. J. Solut. Chem. 3, 377–384. Poisson, A., Gadhoumi, M.H., 1993. An extension of the practical salinity scale 1978 and the equation of state 1980 to high salinities. Deep Sea Res. 40, 1689–1698. Romeo, R., Giuliano Albo, P.A., Lago, S., Brown, J.S., 2017. Experimental liquid densities of cis-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(Z)) and trans-1-chloro-3,3,3trifluoropropene (R1233zd(E)). Int. J. Refrig. 79, 176–182. Safarov, J., Berndt, S., Millero, F., Feistel, R., Heintz, A., Hassel, E., 2012. (p,ρ,T) properties of seawater: extensions to high salinities. Deep-Sea Res. I 65, 146–156. Safarov, J., Berndt, S., Millero, F.J., Feistel, R., Heintz, A., Hassel, E.P., 2013. (p,ρ,T) Properties of seawater at brackish salinities: extensions to high temperatures and pressures. Deep-Sea Res. I 78, 95–101.
4. Conclusion In this work, the density of seawater was measured. Samples of standard seawater of different absolute salinity, SA ¼ (10.044, 30.141, 35.158 and 38.178) g kg 1, provided by OSIL were studied, and the densities were obtained at eight temperatures: from (278.15–313.15) K every 5 K at atmospheric pressure. The measurements were carried out by means of a commercial vibrating tube densimeter (Anton Paar DSA 5000 M), using the substitution method. Seawater and pure water was measured alternatively, in order to correct the measured values by the comparison between experimental pure water density and reference values by Wagner and Pruss (2002). The substitution method allowed to avoid systematic errors of the instrument and drifting effects. The relative uncertainty of seawater density was estimated by considering all the sources of uncertainty and resulted to be 0.003%, with a coverage factor k ¼ 2. With the followed experimental procedure, the main contribution to the uncertainty is due to the repeatability. The perfor mances of the vibrating tube could be evaluated under routinely work ing conditions. Indeed, the uncertainty value obtained in this work is one order of magnitude higher than the one obtained, e.g., by Schmidt et al. (2016), who followed a more sophisticated procedure (e.g., auto matic system for filling). Therefore, with routinely working conditions, vibrating tubes can measure density with a relative uncertainty around 10 5. The experimental densities were compared with the data given by the dedicated equation of state for seawater TEOS-10 (IOC et al., 2010). All the deviations are in agreement with TEOS-10 within 50 ppm. However, experimental densities seem to be systematically higher than TEOS-10. Besides this comparison shows that measurements performed for the sample with absolute salinity of 35.158 g kg 1 are those in better agreement with TEOS-10 since the deviations are within � 10 ppm. This suggests that further investigation of seawater density is needed, espe cially for salinity different from 35.158 g kg 1. The measurements were also compared with preliminary results carried out by Giuliano Albo et al. (2018), by means of a hydrostatic balance for seawater of standard salinity at two temperatures: 283.15 K and 293.15 K. This first com parison showed good agreement (with deviations better than 2 ppm), between measurements performed with the two independent methods. 5
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UNESCO, 1981. The practical salinity scale 1978 and the international equation of state of seawater 1980. In: UNESCO Technical Papers in Marine Science, vol. 36. UNESCO, Paris. Wagner, W., Pruss, A., 2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535. Wright, D.G., Pawlowicz, R., McDougall, T.J., Feistel, R., Marion, G.M., 2011. Absolute salinity, “density salinity” and the reference-composition salinity scale: present and future use in the seawater standard TEOS-10. Ocean Sci. 7, 1–26. Wolf, H., 2008. Determination of water density: limitations at the uncertainty level of 1�10 6. Accred Qual. Assur. 13, 587–591.
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