Thermodynamic Properties of Seawater

Transcription

1 P R E P R I N T ICPWS XV Berlin, September 8, 008 Thermodynamic Properties of Seawater a J. Safarov a,b,*, A. Heintz c, E.Hassel a Lehrstuhl für Technische Thermodynamik, Universität Rostock, 8059, Rostock, Germany. b Azerbaijan Technical University, H. Javid Avn. 5, AZ07 Baku, Azerbaijan. c Lehrstühl für Physikalische Chemie, Universität Rostock, 805, Rostock, Germany. * Corresponding author: javid.safarov@uni-rostock.de (p,ρ,t) data of seawater are measured and a new equation of state will be developed. A new installation using the well known vibration-tube densimeter method was constructed. Calibration procedures were carried out using double-distilled water and well defined aqueous NaCl solutions. A thorough evaluation of the state-of-the-art standard equations for seawater thermodynamic equilibrium properties and a recommendation for improvement of these equations are given. Introduction The majority of water on earth is seawater. Seawater is a solution of salts of nearly constant composition, dissolved in variable amounts of water. For scientific investigations and process design of many natural and technical processes, which have to do with seawater, it is of great importance to have a good base of thermodynamic data. In 006, as a successor of the Joint Panel on Oceanographic Tables and Standards (JPOTS), the Working Group 7 has been established by the International Association for the Physical Sciences of the Ocean (IAPSO) and the Scientific Committee on Oceanic Research (SCOR). Its main objective is a recent evaluation of the current standards for seawater thermodynamics and, if necessary, the recommendation of improved formulations. Among the reasons for this revision process is the need for consistency between seawater properties and the more accurate recent international standards for temperature (ITS-90) and for properties of pure water (IAPWS-95) []. The description equation of seawater equilibrium properties, which is currently in use as the international standard for oceanography, is the 980 International Equation of State of Seawater (EOS- 80), released by the Joint Panel on Oceanographic Tables and Standards (JPOTS), published by UNESCO []. It is based on the temperature scale IPTS-68 and on the Practical Salinity Scale 978, PSS-78 []. According to the analysis of thermodynamic properties of standard seawater, it has to be pointed out, that, after the evaluation of EOS-80, there were no new experimental (p,v,t) measurements available and no other EOS has been developed for the calculation of the thermodynamic properties of standard seawater. The authors of EOS-80 showed that the EOS-80 can be modified, if more reliable data for pure water will become available in the future. The main purpose of our work is the construction of a comprehensive and accurate thermodynamic equation of state over the ranges of interest of parameters in oceanographic research, underwater technology and land-based industrial plants running on seawater and to determine the various thermodynamic properties of seawater with various salinities. This research is necessary in order to provide a sound data base for seawater handling in all kind of technical processes and in calculations which rely on correct seawater properties, like climate model simulations. The constructed equation of state is used for the calculation of the thermal properties. Literature surveys Tait [4] was the first scientist, who studied the volumetric properties of seawater. His measured compressibility results were at temperatures T = (7.5 to 88.5) K and pressures p = (0. to 50) MPa. Ekman [5], in 908, measured the compressions of seawater at T = (7.5 to 9.5) K, p = (0. to 60) MPa and at salinities S = (. and 8.5). Higashi et al. [6], in 9, measured the specific gravity and the vapor pressure of concentrated sea water at T = (7.5 to 448.5) K.

2 Newton and Kennedy [7], in 965, determined the (p,v,t) properties of seawater at T = (7.5 to 98.5) K, p = (0 to 0) MPa and S = (0, 0.5, 4.99 and 4.0). The average uncertainty of specific volume measurements was ±7 0-5 cm g -. Wilson and Bradley [8,9], in 966 and 968, measured the specific volumes of seawater at T = (7.5 to.54) K, p = (0 to 00) MPa and S = (0 to 40.7). The uncertainties of these measurements of specific volume were estimated as ± 0-5 cm g -. Bradshaw and Schleicher [0], in 970, measured the thermal expansion of seawater at T = (7.5 to 0.5) K, pressures p = (0.8 to 00.) MPa and salinities S = (0.5, 5 and 9.5). Temperature derivatives of specific volume were derived; it is estimated that they are accurate to better than ± 0-6 cm g - deg -. Duedall and Paulowich [], in 97, reported isothermal compressibility values of seawater with a precision of ± bar -. The measurements were performed at T = (8.5 and 88.5) K, p = (0 to 90.) MPa and S = 5. Emmet and Millero [], in 974, measured the specific volume of S = 5 salinity seawater at T = (7.5 to.5) K, p = (0 to 99.5) MPa. The specific volumes were fitted to an equation having a standard deviation of ± 0-6 cm g -. The compressibility of distilled water and seawater of S = (0.705, 4.89 and 8.884) salinities were measured by Bradshaw and Schleicher [], in 976, at T = 8.5 K, p = (0.8 to 00) MPa using the well known dilatometer method. The average uncertainty of these literature data has been estimated as v = cm g -. The experimental specific volume results of seawater of Chen and Millero [4], in 976, were presented at T = (7.5 to.5) K, pressures p = (0 to 00) MPa and salinities S = (5 to 40). The uncertainty of specific volume was evaluated as v = cm g -. Caldwell [5], in 978, has measured the temperature-pressure-salinity points at T = (67.07 to 76.99) K, pressures p = (0. to 8.09) MPa and S = (0 to 9.84). After the analysis of all available experimental results of (p,v,t) behavior, isothermal compressibility and thermal expansion, Millero and co-workers [] have evaluated the EOS-80. Experimental The (p,ρ,t) measurements were carried out using a high pressure high temperature vibrating tube densimeter DMA HPM (Anton-Paar, Austria). The schematic principle of the vibration tube densimeter is shown in Fig.. This method is based on the dependence between the period of oscillation of a unilaterally fixed U-tube and its mass [6]. This total mass consists of the U-tube material and the mass of the fluid filled into the tube, respectively the density of fluid times the U-tube volume. The material of the vibration tube is Hastelloy C-76 which consists of a nickel-molybdenum-chromiumtungsten alloy with excellent general corrosion resistance and good fabricability. The characteristic period of oscillation of this model is described by the following equation: m0 + Vρ τ = π, () D where τ is the period of oscillation of the vibration tube, μs; m 0 is mass of the empty vibrating tube, kg; V is volume of the vibrating tube, m ; ρ is sample density, kg m - and D is spring constant, N m -. The period of oscillation measurement and the temperature control is implemented within the DMA HPM control system, which consists of a measuring cell and a modified mpds000v control unit connected to a PC via interface. The temperature in the measuring cell was controlled using a thermostat F-ME (Julabo, Germany) with an error of ±5 mk and was measured using the (ITS- 90) Pt00 thermometer with an experimental error of ± mk.. Pressure was created by a pressure manometer (Type 7-6-0, HIP, USA) and measured by two different pressure transmitters (HP- and P- 0, WIKA Alexander Wiegand GmbH & Co., Germany) with an experimental error of 0.5 and 0.% from a measured value, respectively. The observed reproducibility and estimated maximum uncertainty of the density measurements at temperatures T = (7.5 to 47.5) K and at pressures up to p = 40 MPa is within ± kg m -. All high pressure valves, tubes, fittings etc. were supplied from SETEC and NOVA (Switzerland). Rearrangement of the equation and substitution of the mechanical constants lead to the classical equation for vibrating tube densimeters: ρ = A Bτ, () where: ρ is the sample density, kg m - and τ is the period of oscillation, μs. The parameters A and B were determined by substance calibration measuring the period of oscillation of at least two samples with known density. Water (twice-distillate) [] and NaCl (aq) [7] in various molalities were used as reference substances for the calibration of the installation.

3 Fig. : Vibration tube densimeter installation: Flask for the probe;, 7, 6, 7 Valves;, Fitting; 4 Pressure manometer; 5 Pressure sensor HP-; 6 Pressure sensor P-0; 8 Valve for the closing of system during the experiments; 9 Display mpds000v for the temperature and frequency control; 0 Vacuum indicator; Visual window; Vibration tube; 4 - Interface mode; 5 PC; 8 Thermostate F-ME; 9 Vacuum pump; 0 Thermos for cooling. Unfortunately, the parameters A and B are highly temperature dependent and also pressure dependent. Therefore, the parameters must be determined for each temperature and pressure separately or the classical equation must be expanded with temperature and pressure-dependent terms. For these measurements an extended calibration equation with 4 significant parameters is employed [8]: A = B = i ait + 0 i dit + 0 j b jp + ctp; j eip + ftp () where: a 0, a, a, a, b, b, c, d 0, d, d, d, e, e and f parameters of the equation (). Before starting an experiment only the valve () is closed. The sample filled into the cell () was under vacuum, which is connected to the installation. Vacuum is applied during -4 hours using a vacuum pump S.5 (Leybold, Germany) until a minimal pressure (-5 Pa) has been reached (measured with digital vacuum measurement installation THERMOVAC TM 00 (Leybold, Germany). The valve (7) is closed and the valve () is opened. The investigated substance is filled into the measuring system. The valves () and (6) were closed. The experiments were started usually from the small pressures in the measured cell ( MPa). For temperature stabilization waiting time is about minutes. The period of oscillation of the vibration tube is taken from the display () of mpds000v control system.

4 To check the apparatus and procedures of the measurements, and the accuracy of calibration before engaging in measurements on solutions, the density of double distilled water and aqueous NaCl with various molalities were measured and compared with the values of literature results. An IAPSO Standard seawater sample (S = 4.99 and electrical conductivity k 5 = ) was supplied from the Baltic Sea Research Institute, Warnemünde, Germany. Before the experiments, the sample was very slowly degassed to remove air using the vacuum connection. The experiments were carried out at T = (7.5 to 47.5) K. After each series of experiments the installation was washed with water, methanol and acetone many times and was dried under vacuum. In this case corrosion of the vibration tube is not to be expected. Results The (p,ρ,t) measurements of standard seawater sample (S = 4.99 and k 5 = ) were carried out at T = (7.5 to 47.5) K and pressures up to p = 40 MPa. The temperature and pressure intervals between two experimental points approximately were T = 0 K and p = 0 MPa, respectively. Obtained values were compared with the available literature results of standard sea water at T = (7.5 to.5) K and pressures up to p = 0 MPa and good agreements were received. Equation of state Using a program for standard thermodynamic analysis to describe the (p,ρ,t) properties of seawater, the equation of state (EOS) () from [9] was used: p = A ρ + B ρ 8 + C ρ, (4) where A, B and C are the coefficients of EOS (4) and all are functions of temperature. p is the pressure (MPa) and ρ is the density (g cm - ). The 845 (p,ρ,t) values [7-0,, 4] of seawater sample were tested for checking the correctness of the EOS (4) and an average percent deviation of Δ=±0.008% was found. After these procedures equation (4) was applied to describe the obtained results of standard seawater samples and a maximum percent deviation of Δ = ±0.0% was found. Conclusion The (p,ρ,t) measurements of standard seawater samples were carried out at T = (7.5 to 47.5) K and pressures up to p = 40 MPa. This range of experimental (p,ρ,t) results for standard seawater was covered for the first time and was described by an empirical equation of state. These results will be used for the development of a new equation of state for seawater with various salinities. Obtained results can also be used for oceanographic calculations and marine research. Acknowledgments Financial support from German Science Foundation (HA 6/-) is greatly appreciated. Dr R. Feistel thank for regular discussion of this project. References. W. Wagner and A. Pruß. The IAPWS Formulation 995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, Journal of Physical Chemistry Referent Data,, (00).. N.P. Fofonoff and R.C. Millard. Algorithms for the computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44 (98).. E.L. Lewis and R.G. Perkin. The practical salinity scale 978: Conversion of existing data, Deep-Sea Research, 8A, 07-8 (98). 4. P.G. Tait. Report on some physical properties of fresh water and seawater. The Voyage of H.M.S. Challenger HMSO, Vol. II, Part 4, London, -76 (888). 5. V.W. Ekman. Die Zusammendriickbarkeit des Meerwassers nebst einigen Werien fur Wascr und Quecksilber, Pubs. Circonst. Cons. Perm. Int. Explor. Mcr., 4, -47 (908). 6. K. Higashi, K. Nakamura and R. Hara. The specific gravity and the vapor pressure of concentrated sea water from 0 0 to 75 0, Kogyo Kagaku Zasshi, 4 (Suppl. binding), 7 (9). 7. M.S. Newton and G.C. Kennedy. An experimental study of the P-V-T-S relations of seawater. Journal of Marine Research,, 88-0 (965). 8. W. Wilson and D. Bradley. Specific volume, thermal expansion and isothermal compressibility of seawater. U.S. Naval Ord. Lab. Doc. No. AD, 65-0, 4 pp (966). 9. W. Wilson and D. Bradley. Specific volume of seawater as a function of temperature, pressure, and salinity, Deep-Sea Research, 5,

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