Physical properties of the coexisting phases and thermochemical properties of the H 2 O component in boiling NaCl solutions

Preliminary steam tables that contain data on the physical properties of vapor-saturated aqueous sodium chloride solution and the coexisting gas are given for liquid concentrations between 0 mol NaCl/kg ELO and halite saturation at temperatures between 80° and 325° C. For the same conditions, the tables give the partial molal entropy, enthalpy, and volume of H 20 in the phases. The tables were calculated from parametric equations of state. INTRODUCTION The tables assembled contain data for the following physical properties of aqueous, vapor-saturated sodium chloride solution and for the thermochemical properties of H 20 in the solution: vapor pressure of the liquid density of the liquid specific volume of the liquid specific volume of the coexisting gas partial molal volume of H 20 in the liquid partial molal entropy of H 20 in the liquid difference in the partial molal entropy of H 20 between the gas and the liquid at constant composition of the liquid partial molal entropy of H20 in the coexisting gas partial molal enthalpy of H 20 in the liquid difference in the partial molal enthalpy of H 20 between the gas and the liquid at constant composition of the liquid partial molal enthalpy of H 20 in the coexisting gas Al A2 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS The values are tabulated for solution compositions from 0 mol NaCl/kg H 20 to halite saturation at temperatures from 80° to 325° C. The assembled tables are essentially "steam tables" for vapor-saturated H 2 0-NaCl solutions. The tables presented here are preliminary. The functions upon which they are based represent a reasonably complete analysis of the available data through 1971. Final tables should include the energy content of the solution and the partial molal quantities for NaCl in the solution. Because there is an immediate need for the contained data, they have been made available in this preliminary form. The tables are given as an aid to geochemical and engineering studies related to the geothermal energy program of the United States. They have been prepared in direct response to the suggestions of scientists and engineers at the Conference on Thermodynamics and National Energy Problems (National Academy of Sciences, 1974) and of an Ad Hoc Committee on Geothermal Chemistry (1974) convened by the U.S. Atomic Energy Commission. The research was made possible through the support of the U.S. Office of Saline Water (Agreements No. 14-30-3040) and the geothermal research program of the U.S. Geological Survey. UNITS, SYMBOLS, AND CONSTANTS UNITS AND SYMBOLS USED IN TABLES AND TEXT The chosen units in the tables for measurements of temperature, pressure, specific volume, and density are °C, bars, cm3 g~ 3-, and g cm3 , respectively. These units are the same as those used in several widely referenced steam tables (Bain, 1964; Keenan and others, 1969). The partial molal entropy, enthalpy, and volume are given as J mol" 1 K" 1 , J mol" 1 , and cm3 mol" 1 , respectively, because these are the units most used in thermodynamic calculations. Both weight percent and molal (mol NaCl/kg H20) scales for units of sodium chloride concentration are widely used in engineering and geochemical research. Both scales are used here to achieve maximum use of the tables. The quantities, their symbols, and the associated units used in this text and in the tables are as follows: H20 COMPONENT IN BOILING NaCl SOLUTIONS A3 Quantity Symbol Units density d g cm"3 specific enthalpy h J g"1 molal enthalpy H J mol" 1 Masson's Rule slope in the k cm"(kg HW)) 1 '2/(mol NaCl) 3/2 empirical equation for apparent molal volume mole fraction of NaCl N mol NaCl/ (mol NaCl+mol H,0) pressure p bar (=lx!0r> pascals) molar gas constant R J mol^K"1 specific entropy s J g^K" 1 molal entropy S J mol^K"1 temperature t degrees Celsius, °C T kelvins, K specific volume v cm'g"1 molal volume V cm3 mol" 1 molecular weight W g mol"1 concentration of NaCl in the x mol NaCl/kg H«0 (molal) liquid w wt percent NaCl apparent molal volume of NaCl cm3 mol" 1 in the liquid limiting apparent molal volume 0, cm3 mol" 1 of NaCl in the liquid as derived from Masson's Rule In the text and the tables the following superscripts are used: SVbSPt Connotation G The superscripted quantity is an attribute of the gaseous phase. L The superscripted quantity is an attribute of the liquid phase. (bar) The overscored quantity is a partial molal quantity of the component indicated by the subscript, in the solution. In the text and the tables the following subscripts are used: *SSSS? Connotation 1 The subscripted quantity is a partial quantity for the component H-O. 2 The subscripted quantity is a partial quantity for the component NaCl. 0 The subscripted quantity is an attribute of the pure substance H-0. x The subscripted quantity is an attribute of a solution of constant but undefined composition in the system NaCl-HoO. sat The subscripted quantity is an attribute of a solution that is saturated in halite. c The subscripted quantity is an attribute of the pure substance H20 at the critical point where the properties of the liquid and the gas are identical. A4 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS FUNDAMENTAL CONSTANTS USED IN CALCULATIONS The Committee on Data for Science and Technology (1973) of the International Council of Scientific Unions gives the molar gas constant R as (8.31441 ±0.00026) J mol1 K' 1 . The Commission on Atomic Weights (1972) gives the following atomic weights: H (1.0079 ±0.0001) g mol1 0 (15.9994 + 0.0003) g mol1 Na (22.98977 ±0.00001) g mol1 Cl (35.453 ±0.001) g mol1 From these atomic weights the molecular weights of the components are: H20 PF1 =(18.0152±0.0005) gmol1 NaCl TF2 = (58.4428±0.0010) g mol1 EMPIRICAL CONSTANTS USED IN THE TEXT AND CALCULATIONS The following list gives the constants for the equations presented in the text. The equation numbers and the constants are as follows: Equation 4: at = 5.93582 XlQ6 a2 =-5,19386 XlO5 a3 = 1.23156xlO5 Equation 5: 6 1 = 1.15420X106 6 2 = 1.41254 XlO7 63 =-1.92476xlO8 6 4 =-1.70717 XlO9 6 5 = 1.05390X1010 Equation 6: e0 = 12.50849 e 1 =-4.616913xl03 e2 = 3.193455xlO~ 4 e3 = 1.1965xlO11 e4 =-1.013137xlO2 e5 =-5.7148XlO~ 3 e6 = 2.9370 XlO5 Equation 9: Co =-167.219 Cl =448.55 c 2 =-261.07 H20 COMPONENT IN BOILING NaCl SOLUTIONS A5 S Equation 10: c 3 =-13.644 c4 = 13.97 Equation 11 : c5 =0.315154 ce =~ 1.203374 xlO3 c 7 = 7.48908 XlO13 c8 = 0.1342489 cfl =3.946263 XlO3 Equation 17 : ai} are as follows : i=Q i=l i=2 7 = 0 0.512004 0.611366 8.44104 1 -1.191807 -3.258346 28.86344 2 2.599832 6.393115 -270.10366 3 -21.433083 -6.447504 624.08835 4 15.281761 3.202128 -675.70455 5 -2.527165 -0.514945 363.16788 6 -2.454047 -0.120192 -79.26405 PHYSICAL PROPERTIES OF THE PHASES AND THERMOCHEMICAL DATA FOR H2O SYNOPSIS OF THE THEORETICAL APPROACH In previous research (Haas, 1970; 1971a, b), empirical expressions were presented for the vapor pressure and density of vapor-saturated sodium chloride solutions. Those results were combined with the expressions for the change of the pressure with temperature for a binary liquid of constant composition (Dalton and Barieau, 1968, p. 56, eq. 398) to prepare tables for the thermophysical properties of H20 in the coexisting liquid and gas. ( where the symbols are as defined in the previous section. The terms AS, AV, and &H (eq 2) are the partial molal entropies, volumes, and enthalpies of vaporization of the components indicated by the subscripts. Because the coexisting liquid and gas are at equilibrium, the free-energy difference is zero and equation 1 may be restated : -g A6 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS The partial molal entropy and partial molal enthalpy of H20 in the liquid can be obtained from pressure-temperature-composition and density-temperature-composition functions provided that the products NG -&S2 , NG -&H2) and NG -A?2 are small, and provided that the salt content of the vapor is nil. If the salt content of the vapor is nil, the properties of pure gaseous H20 at the temperature and pressure of the solution may be substituted for the partial molal quantities of H20 in the gas. At 350°C and halite saturation, the vapor contains 8xlO4 mol percent NaCl (Sourirajan and Kennedy, 1962). (Concentration data at 300° C are unavailable, but it would be less than 350°C.) At 300° and halite saturation, the enthalpy of vaporization of NaCl from the solution is estimated to be 15 kJ mol" 1 and the product NG -&H2 is less than 0.1 J mol" 1 (estimated from an analysis of the data in Liu and Lindsay, 1971, and Sourirajan and Kennedy, 1962). The product NG -&S2__is therefore less than 2X104 J mol1 K1 . The product N°-AF2 could riot be estimated. Granting that the above products are small, equations 1 and 2 may be simplified: <2a) In equations la and 2a, the term (7$p/'dT) x may be evaluated from the functions for the vapor pressure of the solution; the terms Si, #1, and V\ from functions for the gaseous H 20; and F! from the function for the density of the vapor-saturated solution. The remaining terms Si and H l may be obtained by substitution of the described functions into equations la and 2a, respectively, and solving the results. VAPOR-PRESSURE FUNCTION Haas (1971a, b) used the reference substance technique as given by Othmer and Yu (1968) and further amplified by Othmer and Chen (1968) to correlate the vapor pressure of solutions of NaCl from 0 molal to halite saturation. From the Clapeyron equations for the vaporization of two liquids, Othmer and coworkers have shown that the temperature of the brine Tx and the temperature H20 COMPONENT IN BOILING NaCl SOLUTIONS A7 of H20 liquid T0 at the same pressure are related by the following equation : In T0 =m In Tx + c (kelvins, K) (3) Refer to figure 1 for a graphical description of the relation beween Tx and T0 at constant pressure. From -11° to 300° C, where precise data are available, the empirical fit was made by setting c = 0 and m= (a+bTx)1 . The terms a an