1449
I n d . E n g . Chem. Res. 1995,34, 1449-1460
Simultaneous Solubility of Ammonia and Carbon Dioxide in Aqueous Solutions of Sodium Sulfate in the Temperature Range 313-393 K and Pressures up to 3 MPa Volker Bieling, Friedhelm Kurz,Bernd Rumpf, and Gerd Maurer" Lehrstuhl fur Technische Thermodynamik, Universitat Kaiserslautern, 0-67653 Kaiserslautern, Federal Republic of Germany
The simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate was measured in the temperature range 313-393 K a t total pressures up to 3 MPa. Experimental results are reported and compared to correlations and predictions. Predicted results generally agree well with experimental data.
Introduction The solubility of weak electrolyte gases such as ammonia, carbon dioxide, sulfur dioxide, or hydrogen cyanide must be known for process design in many applications. Typical examples are applications in the chemical and oil-related industries, the production of fertilizers, and applications in environmental protection. Correlating and predicting the simultaneous solubility of ammonia and sour gases in aqueous phases are difficult tasks due to chemical reactions in the liquid phase resulting in the presence of ionic species. Furthermore, the liquid phase often contains other strong electrolytes, and solid phases might precipitate. Continuing earlier work on the simultaneous solubility of ammonia and sour gases in aqueous phases (Goppert and Maurer, 1988; Muller et al., 1988; Bieling et al., 1989; Rumpf et al., 1993; Kurz et al., 19951, this contribution reports new experimental results for the simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate in the temperature range 313-393 K and total pressures up to 3 MPa. Ammonia, carbon dioxide, and sodium sulfate molalities range up to 4,3.5, and 2 molkg, respectively. A modification of Pitzer's model for the excess Gibbs energy of aqueous solutions of strong electrolytes with interaction parameters as determined in earlier publications (Rumpf and Maurer, 1993a,b; Kurz et al., 1995) on the binary and ternary subsystems was used to predict the new data. The model proves to be able to give reliable estimates for vapor-liquid and vaporliquid-solid equilibria in this extremely complex system over the range of temperature and composition investigated here.
Experimental Section The apparatus and procedure are basically the same as those used in previous investigations (Goppert and Maurer, 1988; Muller et al., 1988; Kurz et al., 1995); therefore, only some essentials are repeated. A thermostated, evacuated cell is filled with a known amount of aqueous sodium sulfate solution. Then, a known amount of ammonia is added and the cell is charged step by step with known amounts of carbon dioxide. After each addition of a gas, the mixture is equilibrated, and temperature, pressure, and gas-phase volume are measured. Furthermore, a small amount of the gas phase is withdrawn from the cell and ~~
* To whom correspondence should be addressed. 0888-588519512634-1449$09.0010
analyzed by gas chromatography. From the results for the composition of the vapor phase, the volume of the vapor phase and the total amounts of each substance charged into the cell, the overall amounts of ammonia and carbon dioxide dissolved in the (liquid solid) phase are calculated (for details see Goppert and Maurer, 1988; Muller et al., 1988). The temperature is measured by resistance thermometry with a maximum uncertainty of k0.1 K. The pressure is determined by a pressure transducer mounted on the bottom of the cell. The uncertainty in determining the total pressure is f0.5 kPa a t pressures up to 0.7 MPa, &lkPa at pressures up to 1.1MPa, and &6 kPa a t higher pressures. The gas chromatographic analysis of the vapor phase was achieved with a column of Hayesep P (Werner Gunther halysentechnik, Dusseldorf? and a thermal conductivity cell. Before and after each series of measurements, the gas chromatograph was calibrated with the pure substances ammonia, carbon dioxide, and water. The calibration was also checked by experiments with binary mixtures. Substances. Ammonia (299.999 mol %) and carbon dioxide (299.995 mol %) were purchased from MesserGriesheim, Ludwigshafen, and used without further purification. Sodium sulfate (299 mass %) was purchased from Riedel de Haen AG, Seelze. The salt was degassed and dried under vacuum. Water was deionized and further purified by vacuum distillation.
+
Results The results for the total and partial pressures above aqueous solutions containing ammonia, carbon dioxide, and sodium sulfate in the temperature range 313-393 K are given in Table 1. As usual, partial pressure is defined as the product of the total pressure and the vapor phase mole fraction. Furthermore, Table 1 contains numbers for the estimated uncertainties in the reported variables and the number of phases in the equilibrium cell. More experimental results, however only for the total pressures above those solutions, are given in Tables 8-10 in the supplementary material (see paragraph a t end of paper). The maximum sodium sulfate molality investigated is 2 molkg; the maximum ammonia molality is about 4 molkg. The carbon dioxide molality ranged up to 3.5 molkg, corresponding to total pressures up to 3 MPa. For some of the solutions investigated, the appearance of a solid phase was observed after the completion of a series of measurements. For some series of measurements, only the total pressure above the aqueous
0 1995 American Chemical Society
1460 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 Table 1. Experimental Results for the Total Pressure and the Partial Pressures of Ammonia, Carbon Dioxide, and Water above Aqueous Solutions Containing Sodium Sulfate
T,K 313.17 313.01 313.22 313.16 313.15 313.16 313.16 313.14 313.14 313.15 313.14 313.14 352.99 353.00 353.00 353.00 353.01 352.95 352.98 353.01 352.96 352.98 352.99 352.95 352.94 352.94 352.93 352.93 352.93 352.94 352.93 352.94 352.95 352.93 352.94 352.94 352.93 352.93 352.94 352.94 352.95 352.91 352.91 393.20 393.20 393.23 393.20 393.20 393.22 393.24 393.20 393.22 393.20 393.21 393.22 393.22 393.21 393.21 393.21 393.22 393.23 393.22 393.15 393.15 393.14 393.14 393.15 393.14 393.14 393.17 393.18 393.16 393.14 393.16 393.16 393.15
H moLkg ~ , 0 2.420 f 0.009 2.421 f 0.009 2.422 f 0.009 2.425 f 0.009 2.427 f 0.009 2.428 f 0.009 2.429 f 0.009 2.429 f 0.009 2.429 f 0.009 2.429 f 0.009 2.429 f 0.009 0 1.933 f 0.009 1.934 f 0.009 1.937 f 0.009 1.941 f 0.009 1.944 i 0.009 1.947 i 0.008 1.949 f 0.008 1.951 i 0.008 1.952 i 0.008 1.953 i 0.008 1.954 i 0.008 1.955 i 0.008 1.956 f 0.008 1.956 f 0.008 0 2.140 i 0.010 4.115 f 0.018 4.117 f 0.011 4.120 f 0.011 4.124 f 0.011 4.128 i 0.011 4.132 f 0.011 4.136 i 0.011 4.142 i 0.010 4.148 f 0.010 4.152 f 0.010 4.157 i 0.009 4.160 i 0.009 4.163 f 0.009 4.164 f 0.009 0 1.489 f 0.013 1.491 i 0.013 1.493 f 0.013 1.496 f 0.013 1.498 i 0.013 1.500 f 0.013 1.503 f 0.013 1.503 f 0.013 0 4.007 f 0.017 4.007 f 0.017 4.008 f 0.017 4.010 i 0.016 4.012 f 0.016 4.016 f 0.016 4.021 f 0.016 4.027 i 0.015 4.032 i 0.015 0 1.977 f 0.016 1.979 f 0.016 1.983 f 0.016 1.988 f 0.016 1.994 f 0.015 1.999 i 0.015 2.003 f 0.014 2.005 f 0.015 2.006 f 0.015 0 3.345 k 0.018 3.345 i 0.018 3.349 i 0.018
~ ~ N ~molkg ~ s o ~~ , N 1.001 i 0.002 1.001 f 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 1.001 i 0.002 0.997 i 0.002 0.997 i 0.002 0.997 i 0.002 0.997 i 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 f 0.002 0.997 i 0.002 0.997 i 0.002 1.001 i 0.002 1.001 2 0.002 1.001 i 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 1.001 f 0.002 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 0.983 f 0.003 1.000 f 0.003 1.000 f 0.003 1.000 f 0.003 1.000 f 0.003 1.000 f 0.003 1.000 f 0.003 1.000 f 0.003 1.000 i 0.003 1.000 f 0.003 1.000 f 0.003 1.990 f 0.004 1.990 i 0.004 1.990 i 0.004 1.990 i 0.004 1.990 i 0.004 1.990 i 0.004 1.990 i 0.004 1.990 f 0.004 1.990 i 0.004 1.991 f 0.004 2.006 i 0.004 2.006 i 0.004 2.006 i 0.004 2.006 i 0.004
ficoz, molkg 0 0 0.188 i 0.003 0.421 f 0.006 0.730 i 0.006 1.095 i 0.006 1.462 f 0.007 1.801 f 0.008 2.105 i 0.009 2.300 i 0.013 2.391 i 0.017 2.449 i 0.022 0 0 0.093 f 0.003 0.243 f 0.006 0.446 i 0.006 0.648 i 0.006 0.810 f 0.006 0.933 f 0.007 1.084 f 0.007 1.181 f 0.008 1.253 f 0.008 1.343 f 0.009 1.479 f 0.011 1.631 f 0.014 1.707 i 0.017 0 0 0 0.134 i 0.003 0.299 f 0.006 0.478 f 0.006 0.695 f 0.006 0.914 f 0.006 1.150 f 0.006 1.439 f 0.006 1.748 i 0.007 2.040 f 0.008 2.357 f 0.009 2.702 i 0.011 3.035 i 0.014 3.232 i 0.018 0 0 0.114 i 0.004 0.316 f 0.009 0.521 i 0.010 0.754 f 0.012 1.009 i 0.016 1.264 i 0.023 1.372 i 0.030 0 0 0.131 f 0.004 0.291 f 0.009 0.580 i 0.009 0.870 f 0.010 1.197 i 0.011 1.632 i 0.012 2.288 f 0.017 2.719 i 0.023 0 0 0.124 f 0.005 0.306 f 0.010 0.558 f 0.010 0.834 f 0.012 1.153 f 0.015 1.420 f 0.019 1.600 f 0.027 1.755 f 0.037 0 0
0.155 i 0.005 0.369 i 0.010
~ O ~ N MPa H ~ , 0.122 f 0.011 0.109 f 0.011 0.088 f 0.010 0.056 f 0.013 0.028 f 0.011 0.010 f 0.009 0 0 0 0
10pcoz,MPa
0
0 0 0.002 i 0.006 0.009 f 0.006 0.055 i 0.011 0.247 f 0.011 0.915 i 0.013 2.689 f 0.014 4.564 f 0.013 6.751 f 0.013
0.404 i 0.019 0.384 i 0.018 0.331 i 0.019 0.266 i 0.017 0.206 i 0.014 0.158 i 0.011 0.126 i 0.010 0.090 i 0.010 0.072 i 0.009 0.061 i 0.009 0.047 i 0.009 0.030 i 0.008 0.015 i 0.008 0.010 i 0.008
0 0.005 f 0.004 0.022 f 0.005 0.065 f 0.007 0.136 f 0.009 0.229 f 0.012 0.432 f 0.018 0.636 f 0.022 0.848 f 0.025 1.221 f 0.028 2.157 f 0.032 4.228 f 0.035 6.075 f 0.036
0.452 i 0.020 0.876 i 0.025 0.838 i 0.025 0.786 i 0.027 0.724 i 0.027 0.657 i 0.026 0.582 i 0.025 0.507 i 0.023 0.409 i 0.021 0.315 i 0.017 0.234 i 0.014 0.162 i 0.010 0.103 i 0.010 0.061 i 0.009 0.043 i 0.008
0 0.002 f 0.004 0.005 f 0.004 0.013 f 0.005 0.026 f 0.005 0.050 f 0.006 0.103 f 0.008 0.215 f 0.011 0.424 f 0.017 0.880 f 0.024 1.918 f 0.031 4.020 f 0.034 6.338 f 0.035
0.883 i 0.057 0.803 i 0.056 0.650 i 0.046 0.492 i 0.038 0.336 f 0.027 0.212 i 0.040 0.038 i 0.040 0.034 f 0.040
0.019 f 0.010 0.215 f 0.018 0.783 f 0.054 2.328 f 0.105 6.691 f 0.170 18.473 f 0.249 27.973 f 0.267
2.335 f 0.098 2.247 i 0.102 2.147 i 0.100 1.965 i 0.095 1.795 f 0.093 1.538 f 0.090 1.143 i 0.078 0.708 i 0.058 0.398 f 0.033
0.003 f 0.009 0.029 f 0.010 0.148 f 0.016 0.412 f 0.033 0.966 f 0.067 2.471 f 0.122 8.583 i 0.218 18.785 f 0.228
1.528 f 0.070 1.411 f 0.071 1.216 f 0.065 0.973 f 0.057 0.702 f 0.047 0.447 f 0.034 0.287 f 0.023 0.170 f 0.046 0.139 f 0.044
0.005 f 0.009 0.063 f 0.012 0.316 f 0.024 1.070 f 0.063 3.403 f 0.114 8.419 f 0.146 17.017 i 0.219 28.897 f 0.244
2.481 f 0.087 2.402 f 0.091 2.205 f 0.089
0.003 f 0.009 0.037 i 0.011
1 0 p ~ ~MPa 0, 0.071 f 0.005 0.064 f 0.009 0.067 i 0.009 0.068 f 0.010 0.070 f 0.014 0.070 f 0.014 0.068 f 0.013 0.063 f 0.008 0.064 f 0.009 0.064 f 0.009 0.061 f 0.008 0.062 f 0.009 0.455 f 0.005 0.425 f 0.019 0.421 f 0.019 0.427 f 0.020 0.432 i 0.019 0.431 i 0.017 0.434 i 0.016 0.434 i 0.017 0.429 i 0.019 0.428 i 0.020 0.428 i 0.021 0.424 i 0.022 0.423 i 0.023 0.425 i 0.024 0.428 i 0.025 0.454 i 0.005 0.423 i 0.020 0.398 i 0.023 0.399 i 0.023 0.400 i 0.024 0.405 i 0.024 0.401 i 0.023 0.407 i 0.023 0.405 i 0.022 0.412 i 0.021 0.415 i 0.019 0.416 d= 0.019 0.410 i 0.020 0.402 i 0.022 0.412 i 0.023 0.403 i 0.023 1.918 i 0.010 1.859 i 0.061 1.857 i 0.064 1.849 f 0.060 1.847 f 0.074 1.876 f 0.103 1.940 f 0.144 1.952 f 0.168 2.079 f 0.181 1.918 f 0.010 1.834 f 0.097 1.846 f 0.100 1.866 i 0.099 1.854 i 0.095 1.869 f 0.096 1.896 f 0.101 1.900 f 0.116 1.841 i 0.148 1.810 f 0.154 1.868 f 0.005 1.758 f 0.071 1.764 f 0.073 1.775 i 0.069 1.844 f 0.067 1.812 f 0.077 1.776 f 0.100 1.874 f 0.125 1.731 f 0.134 1.973 f 0.154 1.868 i 0.005 1.716 f 0.085 1.709 f 0.088 1.756 i 0.087
lop, MPa 0.071 f 0.005 0.186 f 0.005 0.175 f 0.005 0.156 f 0.005 0.128 i 0.005 0.108 i 0.005 0.133 i 0.005 0.309 i 0.005 0.979 i 0.005 2.753 f 0.005 4.625 f 0.005 6.812 f 0.005 0.455 f 0.005 0.829 f 0.005 0.805 f 0.005 0.763 f 0.005 0.720 f 0.005 0.702 f 0.005 0.727 f 0.005 0.788 f 0.005 0.951 f 0.005 1.136 f 0.005 1.337 f 0.005 1.693 f 0.005 2.610 f 0.005 4.667 f 0.005 6.513 f 0.005 0.454 f 0.005 0.875 f 0.005 1.274 f 0.005 1.237 f 0.005 1.187 f 0.005 1.134 f 0.005 1.071 f 0.005 1.015 f 0.005 0.962 f 0.005 0.924 i 0.005 0.945 i 0.005 1.073 i 0.005 1.452 i 0.005 2.423 i 0.005 4.493 f 0.005 6.784 i 0.005 1.918 i 0.010 2.742 i 0.010 2.680 i 0.010 2.714 i 0.010 3.121 i 0.010 4.540 f 0.010 8.843 i 0.010 20.463 i 0.060 30.086 i 0.060 1.918 i 0.010 4.168 i 0.010 4.097 i 0.010 4.042 f 0.010 3.967 i 0.010 4.077 f 0.010 4.401 f 0.010 5.513 f 0.010 11.132 f 0.060 20.993 f 0.060 1.868 f 0.005 3.286 i 0.010 3.180 f 0.010 3.053 i 0.010 3.133 f 0.010 3.584 f 0.010 5.626 f 0.010 10.581 f 0.010 18.918 f 0.060 31.009 f 0.060 1.868 f 0.005 4.197 f 0.010 4.113 f 0.010 3.998 f 0.010
NP 2 2 2 2 2 2 2 2 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 3 2 2
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1451 Table 1. (Continued)
T,K 393.16 393.16 393.15 393.16 393.14 393.15
fiNazSO,,
molflrg
2.006 f 0.004 2.006 f 0.004 2.006 f 0.004 2.006 f 0.004 2.006 f 0.004 2.006 f 0.004
% N H ~ , moVkg
%con,molflrg 0.671 f 0.010 1.015 f 0.011 1.586 f 0.014 2.092 f 0.019 2.390 f 0.026 2.600 f 0.034
3.355 f 0.018 3.362f 0.017 3.374f 0.017 3.382i 0.016 3.386 i 0.016 3.387 k 0.016
~ O ~ N MPa H~,
10pco2,MPa 0.174f 0.016 0.561 f 0.040 2.514f 0.109 7.894f 0.156 16.290f 0.199 26.430 f 0.216
1.910 f 0.083 1.540 f 0.079 0.943 f.0.064 0.575 i 0.044 0.350f 0.029 0.305 f 0.025
1 0 ~ ~MPa ~0,
lop,MPa
Np
1.784 f 0.083 1.814f 0.083 1.775 f 0.097 1.845 f 0.123 1.693f 0.129 1.865f 0.143
3.868f 0.010 3.914 f 0.010 5.232 & 0.010 10.313i 0.010 18.333i 0.060 28.599 f 0.060
2 2 2 2 2 2
0 2.4
a
I \
2
a' ' 1.8
Q
1.2
0.6
I
0
1
0
I
2
3
I
II
0
1
00 I
2 co2
Figure 1. Total pressure in the system N H ~ - C O Z - N ~ Z S O ~ - H ~ O a t 393 K and ~ ~ N ~=, 1s omoYkg: ~ (0, 0 ) experimental results, this work; (- - -1 calculated results for the system NH3-CO2HzO, Kurz et al. (1995);(-) prediction, this work.
solution was measured. For these data points, the carbon dioxide and ammonia molalities in the liquid phase were corrected for the gas present in the vapor phase of the cell by using calculated results for the composition of the vapor phase. With the measured volume of the gas phase, the measured total pressure and mole fractions in the gas phase calculated with the model presented below, the amounts of gas dissolved in the liquid phase were calculated in an iterative procedure. The use of calculated instead of measured mole fractions in the vapor phase increases the uncertainty in the overall molalities of ammonia and carbon dioxide in the liquid phase by about 0.1% and 0.3%, respectively. As an example, the total pressure and the partial pressures of ammonia and carbon dioxide above a 1 m solution of sodium sulfate at 393 K are plotted in Figures 1-3 versus the overall amount of carbon dioxide present in the liquid phase. Two series of measurements with nearly constant overall amounts of ammonia in the liquid phase of about 1.5 and 4 moVkg are shown. The broken lines represent calculated results for the salt-free system ammonia-carbon dioxide-water (Kurz et al., 1995). Adding carbon dioxide to an ammoniacal, sodium sulfate containing solution at constant temperature and constant overall molalities of ammonia and salt in the liquid phase at first results in a slight decrease in the total pressure as most of the carbon dioxide is dissolved chemically. After passing a minimum, a steep increase in the total pressure is observed. Increasing the amount of ammonia in the liquid phase shifts the minimum toward higher overall amounts of carbon dioxide.
/(mol/kg)
Figure 2. Partial pressure of ammonia in the system NH3-COzo , (0, 0 ) experiNazS04-HzO at 393 K and ~ ~ N ~=~ 1s moVkg: mental results, this work; (- - -) calculated results for the system NH3-COz-Hz0, Kurz et al. (1995);(-1 prediction, this work.
28
21
14
7
0 0
1
2
Figure 3. Partial pressure of carbon dioxide in the system NH3COz-NazS04-HzO a t 393 K and = 1 molkg: (0, 0 ) experimental results, this work; (- - -) calculated results for the system NHs-COz-HzO, Kurz e t al. (1995);(-) prediction, this work.
The partial pressure of ammonia (cf. Figure 2) decreases with increasing amount of the sour gas in the liquid phase as more and more ammonia is converted into ionic, nonvolatile form (ammonium or carbamate ions). The partial pressure of carbon dioxide at first is
1462 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
I
vapor NHs
COz
H2O
t NH3
dissociations of ammonia, carbon dioxide, and bicarbonate, the formation of carbamate, and the autoprotolysis of water:
’’I
t + HzO + NH:
+ H,O CO, + H,O
NH,
-t OH-
(1) COz + Hz0 + HCO, Hf (2) HCO; e COi- + Hf (3) NH;I + HCO, + NHzCOO- HzO (4) HzO H+ + OH(5) NaZS04 + 2 . Nat + SO:salt j salt k
t-++-l I
salt i
salt j salt k
NH4+ + OH-
(1)
+ H+
(2)
HCO,-
+
+
salt i
--L
....
liquid
....
NH3 + HCO,H,O
”
solid ’
---L
NH,COO-
H’
+ H,O
(4)
+ OH-
(5)
Sodium sulfate is assumed to be fully dissociated. The condition for chemical equilibrium yields the following equation for a chemical reaction R: I
Figure 4. VLE, SLE, and chemical reactions in the ammoniacarbon dioxide-sodium sulfate-water system.
very small and increases rapidly when in the liquid phase ammonia has been spent by chemical reactions (cf. Figure 3). Thus, the behavior of the quaternary system is very similar to that observed for the salt-free system (cf. Goppert and Maurer, 1988; Muller et al., 1988). But sodium sulfate causes significant effects: As can be seen from Figure 2, ammonia is salted out by sodium sulfate, i.e., the partial pressure of ammonia above the saltcontaining solution is larger than that above the saltfree solution. The effect decreases with increasing amount of the sour gas present in the liquid phase. However, as shown in Figure 3, carbon dioxide is salted in,i.e., the partial pressure of carbon dioxide above the salt-containing solution is below that above the saltfree solution. Without ammonia, carbon dioxide is salted out by sodium sulfate (cf. Rumpf and Maurer, 1993a). The change from salting out to salting in in the presence of ammonia is due to the strong influence of sodium sulfate on the chemical reactions in the liquid phase. The partial pressure of water is reduced by sodium sulfate, but it is only slightly changed when both gases are dissolved. For the total pressure, salting out is observed at low carbon dioxide concentrations-mainly due t o the enhancement of the partial pressure of ammonia-whereas at higher molalities the increasing salting in of carbon dioxide and decreasing salting out of ammonia results in a lower pressure than that above the salt-free solution. Thus, for example, for a solution containing 1.49 mol of ammonia and 1 mol of carbon dioxidekg of water, the total pressure above a 1 m sodium sulfate solution is about 0.89 MPa, whereas it is 1.4 MPa above the salt-free solution, Le., the reduction is about 36%.
1
The existence of solid (hydrated or unhydrated) salts Mv+Xv-w,H20 is considered through the equilibrium condition v-
KM,+y-.VwHzO(T)
vw
(7)
= aL+ax2-aw
Only solids Na2S04, NH4HC03, (NH4)zS04, and NaHC03 were taken into account. In principle, the formation of other solid species, for example, NazC03, (NH&C03*H20or NanSOslOHzO, is also possible. However, as the solubility of these salts is either much higher (cf. Linke and Seidell, 1965) or the salts dehydrate in the temperature range investigated here, no other solids were considered. Assuming the above-mentionedsalts to be present as solids, the following conservation equations for the overall amounts of ammonia, carbon dioxide, water, and sodium and sulfate ions present in the (liquid solid) phases were applied:
+
-
ANH, - ~
” N H+~n ” ~ ~ + 4 ~+” N H ~ C O O+ - ~ ’ N H , H C O+ ~
~~’(NH,),so,
(8)
Modeling Figure 4 shows a scheme of the model applied t o predict the simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate. The model is an extension of the thermodynamic framework presented recently t o correlate the simultaneous solubility of ammonia and carbon dioxide in pure water (Kurz et al., 1995). Due t o chemical reactions in the liquid phase, ammonia and carbon dioxide are present not only in the liquid phase in neutral but also in ionic, nonvolatile form. Five chemical reactions are considered: The
The condition for electroneutrality in the liquid phase yields n“NH4+
+ n”HA + n ” N a + = n ” O H - + n”HC0,- + 2n”co32-+ n ” N H z C 0 0 - + 2n”so42- (13)
The condition for solid-liquid equilibrium (eq 7) has to be taken into account only when in a preliminary calculation-where the formation of solid phases was neglected-the right-hand side of eq 7 turned out to be
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1453 Table 2. Equilibrium Constants for Chemical Reactions 1-5 (313.15 5 T/K 5 473.15) (Edwards et al., 1978; Bieling et al., 1989)
+
AR l n & = - BR ln(T/K) ( T/K)
+ +
-
+ +
NH3 HzO NH4+ OHCOz H2O * HC03- H+ HC03- * COS’H+ NH2COONH3 HC03HzO * H+ OH-
+
+
+
+ H2O
+ CR(T/K)+ DR
-5930.7 -7742.6 -8982.0 552.69 -13445.9
larger than the left-hand side. Thus, the calculation was performed as follows: In the first step, any solid phase was neglected. Therefore, eq 7 is not taken into account and all mole numbers n’i in eqs 8-12 are set to zero. The remaining equations are solved by an iterative procedure yielding a first approximation for the “true”composition of the liquid phase. In the next step, the right-hand side of eq 7 is calculated for each of the solid species considered here. When the right-hand side proved to be larger than the left-hand side, that salt has to be considered as a solid phase. When more than one solid phase is detected in that step, t o a first approximation only that salt with the smallest solubility product is considered to be present as a solid species. At next, the set of equations including the equilibrium condition for the selected solid salt is solved again, thus yielding the composition of the liquid phase as well as the number of moles of the solid species. When no further solid phase is detected, the calculation is finished; otherwise, the calculation has to be repeated again. Thus, the iteration scheme allows the calculation of the composition in the liquid phase, the number of phases as well as the mole numbers of the solid species. Having determined the composition of the liquid and solid phases, the composition of the vapor phase is calculated from
-15.063 -14.506 -18.112 -4.0400 -22.4773
~~~
NH3 C02
3.932 192.876
e;)
-1879.02 -9624.4
-355134.1 0.01441
-28.749
Smith (1980) (cf. Table 5 ) . The mixed second virial coefficients B i j and the partial molar volumes of the gases dissolved in water were calculated according to proposals by Hayden and OConnell(1975) and Brelvi and O’Connell (19721, respectively. As in previous work, activity coefficients of both neutral and ionic species were calculated adapting the method of Pitzer (1973) for the excess Gibbs energy of an aqueous electrolyte mixture:
and fz are functions of ionic strength I and Z i j , k are binary and ternary interaction parameters. The resulting expressions for the activity of a dissolved species and of water are summarized in Appendix 1. To apply eq 16, the dielectric constant of pure water and interaction parameters ply, ply, and r i j , k have t o be known. The dielectric constant of pure water was taken from Bradley and Pitzer (1979) (cf. Appendix 3). The various interaction parameters can be divided into five groups: (1) Parameters describing the binary subsystems gas-water: For NH3-Hz0, the interaction parameter ,Bgi ,NH was obtained from Rumpf and Maurer (1993b) (cf. $able 6). As the molality of carbon dioxide remains small even at higher pressures, the interaction parameter p$A2,co,was set to zero. ~ l ternary l interaction parameters between neutral solutes were neglected. (2) Parameters for the binary subsystems saltwater: For NaHC03-HzO and NazC03-Hz0, interaction parameters were obtained from Peiper and Pitzer (1982). For (NHdzS04-HzO and NazS04-Hz0, parameters were taken from Rumpf and Maurer (1993a) and Rogers and Pitzer (1981), respectively (cf. Appendix 2). (3) Parameters describing interactions in the ternary system NH3-COz-HzO were taken from the recent work of Kurz et al. (1995). They are summarized in Table 6. where
The calculation requires the knowledge of five temperature-dependent equilibrium constants K I - K ~the , soluthe activity coefficients of bility products KM,,+X,-.Y,H~O, all species present in the liquid phase, Henry‘s constants for ammonia and carbon dioxide in pure water, the vapor pressure and the molar volume of water as well as information on the vapor-phase nonideality, and the partial molar volumes of the dissolved gases. The equilibrium constants K1-K5 were taken from Bieling et al. (1989) (cf. Table 2). Henry‘s constants for ammonia and carbon dioxide were obtained from Bieling et al. (1989) and Rumpf and Maurer (1993a), respectively (cf. Table 3). The solubility products for NazS04, (NH&S04, and NH4HC03 were taken from Rumpf and Maurer (1993b) and Kurz et al. (1995), respectively (cf. Table 4). For NaHC03, the solubility product was calculated from the equations of Brewer (1982) (cf. Appendix 5). The vapor pressure and the molar volume of water were taken from Saul and Wagner (1987) (cf. Appendix 4). A truncated virial equation of state was used to calculate fugacity coefficients. Pure component second virial coefficients Bi,i were calculated from a correlation based on data recommended by Dymond and
97.976 102.28 116.73 19.817 140.932
Table 3. Henry’s Constant for the Solubility of Ammonia and Carbon Dioxide in Pure Water (273.15 5 T/K 5 473.15) (Bieling et al., 1989; Rumpf and Maurer, 1993a)
fi
pig’, p:? and i = NH,, CO, (15)
-1.1127 -2.8 104 -2.2249 0.46898 0
1454 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 Table 4. Solubility Constants for Ammonium Hydrogen Carbonate, Sodium Sulfate, and Ammonium Sulfate (Rumpf and Maurer, 1993b; Kurz et al., 1995)
A In K, = 8+ B , ln(T/K)+ C,(T/K)+ D,
(TK)
NH4HC03 NazS04 (NH4)zS04
8.3413 6561.6 28179.9
--2465.32 -0.13442 -0.3146
60.36 193.697
Table 5. Pure-Component Second Virial Coefficients (273.15 5
coz
HzO
4.059 65.703 -53.53
-117.713 -184.854 -39.29
405.6 304.16 647.3
353.15 473.15 473.15
follows: In parameter &L'N, H$+ was set to zero and the remaimng parameters determined from eq 17:
T/K5 473.15)
(0) BC0,,SO42-
NH3
298.15 308.15 298.15
-326.526 -1104.258
2.5 1.4 4.3
(4) Parameters describing interactions between a
neutrally dissolved gas (NH3 or COS) and dissolved strong electrolytes (Na~S04or (NH&SOd): When a single, nonreacting gas is dissolved in a n aqueous solution of a strong electrolyte M,+X,-, due to the condition of electroneutrality only certain "observable" combinations of interaction parameters can be determined:
B%,,Na+
(0)
= BC0,,(NH4)2S04
= 1~S(B%Z,Na,S04 - B(0) COz,(NH4i,S0,)
(20)
(2
As only a very small amount of neutral carbon dioxide is present, ternary parameters including interactions between two carbon dioxide molecules were neglected: 'CO,,CO,,M
= 'CO,,CO,,X
=
(22)
Furthermore, all ternary parameters for interactions between a neutral solute G and two ions carrying the same charge were also neglected: zG,M,M
= ZG,KX = 0;
G = C02, NH,
(23)
Only two ternary parameters for interactions with carbon dioxide were considered: 'C0,Na+,S042~ G , G , M X= V+'G,G,M
+ V-'G,G,X
(19)
Thus, certain binary and ternary parameters in the above equations can be set to zero without losing any generality. As parameters in the ternary subsystem NH3-COz-HzO were determined relative to @)NH + = 0, parameters describing interactions between carbon dioxide and sodium or sulfate ions were determined as
= 1~4rCOz,Na,S04,Na2S04
(24)
~COz,NH4+,S04z-= 1 ~ ~ ~ C 0 , , ~ N ~ 4 ) , ~ 0 4 , ( N (25) H4~z~04
B(0) COz,Na2S04,
B(0)
~ C O Z , N ~ Z ~ O ~ , N ~ ~and SOU taken from investigations on the solubility of carbon dioxide in aqueous solutions of those salts (Rumpf and Maurer, 1993a). Experimental results for the solubility of ammonia in aqueous solutions of sodium and ammonium sulfate C0,,(NH4i,S04,
rC0z,(NH4)2S04,(NH4j~S04 were
Table 6. Interaction Parameters To Predict VLE and VLSE in the Ammonia-Carbon Dioxide-Sodium Sulfate-Water System
-0.034 0.2857 -0.3391 -0.03933 0.0843 0.1134 -0.146 -1.1264 x low3 5.0715 x 1.4007 x -9.75 x 10-2 3 10-3 0.0071 0.00167 10-4 -2 x 10-4 -0.1666 0.7790 -1.7475 x -2.0811 x
14.59 -99.47 151.28 25.26 -16.15 -45.70
47.13 44.23 -3.76 -1.23 0.0984 -0.1968 110.66 -446.70
273
473
NH3-Hz0
313
473
NH3-COz-HzO
393
NH3-NazS04-HzO NH~-(NH~)zSO~-HZO
433
COz-NazS04-HzO COZ-(NH~)ZSO~-HZO
7
1
-11347.5 78895.4
I
313
313
(Rumpf and Maurer, 1993b) were used analogously to calculate the remaining parameters for interactions of ammonia with sodium or sulfate ions:
(26)
042
%
> s
T / K = 393 fiNqSO,/(mol/kg)
/
= 2.0
I
35 '0
28
/
I
o
Ternary parameters including ammonia and sodium or ammonium sulfate were assigned in the same way as those including carbon dioxide: ZNH3,Na+,S042- = 1~4rNH3,Na,S0,,Na,S0,
(28)
But, as a t low carbon dioxide concentrations a large amount of neutral ammonia may be present together with sodium and sulfate ions, ternary parameters ZNH,,NH,,N~+ and ZNH,,NH,,SO~Z- had to be taken into account. They were calculated from data on the solubility of ammonia in aqueous solutions of sodium sulfate and ammonium sulfate (cf. Rumpf and Maurer, 1993b) by setting Z N H ~ , N H ~ , N H ,equal + to zero: ZNH,,NH,,SO,~'NH,,NH,,Na-
= ~NH,,NH,,(NH,),so,
= 1/2(rNH3,NH,,Na,S0,
(30)
- rNH,,NH,,(NH4),S0,)
(31) The parameters are given in Table 6 . For the system N H 3 - ( N H 4 ) 2 S 0 4 - H 2 0 the parameter set published earlier (Rumpf and Maurer, 1993b) was reevaluated including new experimental results at low temperatures. These will be published in a future publication. ( 5 ) Parameters resulting in higher order correction terms in the excess Gibbs energy, e.g., parameters describing effects from unsymmetrical mixing: These parameters can hardly be obtained from the available experimental information; to a first approximation, they were therefore neglected. The resulting set of parameters as given in Appendix 2 and Table 6 allows a prediction of the simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate. In Figures 5-7, two series of measurements at 393 K and at a salt molality of 2 molkg but different ammonia molalities of about 2 and 3.4 molkg are compared to calculations for the salt-free system NH3C 0 2 - H z O as well as to predictions for the quaternary system. Increasing the sodium sulfate molality at constant temperature and constant overall amounts of the dissolved gases results in a more pronounced salting out effect a t low molalities of carbon dioxide and a more pronounced salting in effect at higher carbon dioxide concentrations. For the solution containing about 3.4 molkg ammonia in the liquid phase, the model predicts the carbon dioxide free state to be in three-phase equilibrium (solid phase: sodium sulfate). Therefore, the predicted solubility limit for the precipitation of sodium sulfate is also shown in Figure 5. The model predicts that the addition of carbon dioxide t o an ammoniacal, sodium sulfate containing solution in three-phase equilibrium causes the solid phase to disappear. This seems to be reasonable as neutral ammonia decreases the solubility of sodium sulfate (cf. Rumpf and Maurer, 1993b). But, as with increasing amount of carbon dioxide ammonia originally dissolved in neutral form is converted into ionic form, the solid phase disappears.
0
I
I
1
2
3
5COZ /(mol/kd Figure 5. Total pressure in the system NH3-COz-Na2S04-H20 ~ s o (0, ~ 0 ) experimental results, a t 393 K and ~ ~ N =~2 molkg: this work; (- - -1 calculated results for the system NHs-COzHzO, Kurz et al. (1995); (-1 prediction, this work (- -) predicted solubility limit for the precipitation of NazS04. 0 2.8
a I
calc. solubility limit for the precipitation of N%SO,
\
2
n' '
s
T/K fiw.,so,
= 393 /(mol / k d = 2.0
2.1
1.4
0.7
0
I
I
I
I
1
I
0
1
2
i
Figure 6. Partial pressure of ammonia in the system NHs-COzNazSOd-HzO a t 393 K and ~ ~ N =~2 mol/kg: ~ s o (0, ~ 0 ) experimental results, this work; (- - -1 calculated results for the system NH3-COz-Hz0, Kurz et al. (1995); (-) prediction, this work.
The model is able to predict the observed effects quantitatively. Only at high amounts of carbon dioxide in the liquid phase, the model tends t o underestimate the salting in effect on carbon dioxide. However, it should be noted that the increase in the total pressure curve is very steep at high amounts of the sour gas; therefore, even very small uncertainties in predicting the amount of carbon dioxide dissolved in neutral form may cause large uncertainties in the prediction for the total pressure. Figures 8-10 are to discuss the effects observed at 313 K. Experimentally determined pressures for three overall ammonia molalities of about 1.8, 2.4,and 3.6 moVkg and a fixed overall molality of sodium sulfate of
1456 Ind. Eng. Chem. Res., Vol. 34,No. 4, 1995
9
0.10
0.08
0.06
0.04 0.02 0.00 0
0.5
1.5
1
MC0,
Figure 7. Partial pressure of carbon dioxide in the system NH3COz-NazS04-HzO a t 393 K and "anSol = 2 mol/kg: (0, 0) experimental results, this work; (- - -1 calculated results for the system NH3-COz-Hz0, Kurz et al. (1995); (-1 prediction, this work.
2
.5
/(mol /kg)
Figure 9. Partial pressure of ammonia in the system NH3-COz, moYkg: (0) experimental NazS04-HzO a t 313 K and A N ~ ~ s=o 1 results, this work; (- - -)calculated results for the system NH3C0z-Hz0, Kurz et al. (1995); (-1 prediction. this work.
calc. solubility limit for the precipitation
I ,
+ 5
1
b
2
2.5
Mco, /(mol /kg) Figure 10. Partial pressure of carbon dioxide in the system NH3Figure 8. Total pressure in the system N H ~ - C O Z - N ~ ~ S O ~ - H Z O COZ-NazS04-HzO a t 313 K and A N ~ ~=s 1o molkg: ~ (0) experiat 313 K and ~ ~ L ~ = L N1molkg: ~~so~ (0,0,U) experimental results, mental results, this work (- - -) calculated results for the system this work; (- - -1 calculated results for the system NHs-COzHzO, Kurz et al. (1995);(-1 prediction, this work; (- -1 predicted solubility limit for the precipitation of NaHC03.
1moVkg are compared to predictions. At that temperature, the model predicts the formation of solid sodium hydrogen carbonate at large amounts of carbon dioxide dissolved in the liquid phase. Therefore, the predicted solubility limit for NaHC03 is also shown. The appearance of solid NaHC03 was confirmed experimentally by analyzing the solid phases withdrawn from the cell aRer the completion of each of the series of measurements. As can be seen from those figures, the model predicts that with increasing ammonia molality in the liquid phase an increasing amount of carbon dioxide is needed to cause precipitation of NaHC03. This seems to be reasonable as-with increasing amount of ammonia
NH3-COz-Hz0,
Kurz et al. (1995); (-1 prediction, this work.
dissolved in the liquid phase-more carbon dioxide is converted into carbonate and carbamate ions rather than into bicarbonate ions. At that temperature, only small effects on the total and partial pressures are caused by the salt. The data for the total pressure are predicted with an average absolute deviation of 17.6 W a , those for the partial pressure of ammonia and carbon dioxide with average deviations of 0.4and 18 W a , respectively. A summarized comparison between predicted and measured total and partial pressures is given in Table 7. In most cases, the model gives a good representation of the experimental results. The average relative devia-
Ind. Eng. Chem. Res., Vol. 34,No. 4,1995 1457 Table 7. Comparison between Experimental and Calculated Results (Data Points with p Omitted) no. of data points av re1 dev, % fiNazS04, fiNH3,maxt IfiC02,max, T,K
momg
moVkg
molflrg
313 353 393 393 313 313 353 353 393 393 393
1 1 1 2 0.5 1 0.5 1 0.5 1 2
2.4 4.2 4.0 3.4 3.7 3.6 3.6 3.6 3.6 3.6 3.6
2.5 3.2 2.7 2.6 3.5 3.5 2.8 2.8 1.6 1.7 1.9
P 4 26 15 16 10 12 28 16 13 19 15
I
PNH~
pcoZ
6 9 10
4 10 9 10
pW
15 16
P 12.3 9.4 3.5 9.2 19.5 11.8 5 15 1.4 1.9 3.0
PNH~
pcoZ
1.6 6.7 10
12.4 26 4.2 15
5 50
pW
3.3 3.8
kPa and pi
5 50 kPa
av abs dev, bar P 0.18 0.33 0.31 1.5 0.29 0.2 0.2 0.6 0.07 0.09 0.15
PNH3
PCOz
0.004 0.01 0.07 0.09
0.18 0.32 0.20 1.37
PW 0.004 0.012 0.06 0.07
example once again demonstrates that even very small uncertainties in predicting the composition of the liquid and solid phases might lead to an appreciable uncertainty in the predicted concentration of neutrally dissolved carbon dioxide and consequently also in the predicted pressures.
Precipitation of
6 7 n
P 8
Conclusions
W
\
E-
0
1
2
3
4
5
@,?/(mofig) Figure 11. Predicted species distribution in the ammonia-carbon dioxide-sodium sulfate-water system at 313.15 K, A N H=~4 mol/ kg and f i ~ =~1m~o a g~ : (1) 0 NH3; ~ (2) COz; (3) NH4+; (4) HC03-; (5) c0z2-;(6) NHzCOO-; (7) Na+; ( 8 ) Sod2-; (9) NaHC03 (s).
The simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate has been measured in the temperature range from 313 to 393 K a t total pressures up to 3 MPa and up to 2 m salt solutions. A model to predict the simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate is presented. With interaction parameters determined solely from binary and ternary subsystems, the model is able to quantitatively predict the effects caused by sodium sulfate in this complex, chemically reactive system over a wide range of temperature and composition.
tions in the total pressure typically range from 1 to 9%, Acknowledgment those for the partial pressures of ammonia and water from 2 to 8.5% and 3 to 5%, respectively. For some Financial support of this investigation by the governseries of measurements, larger average deviations in the ment of the Federal Republic of Germany (BMFT total pressure and the partial pressure of carbon dioxide Grants 0326558 A and C), BASF AG, Ludwigshafen, are observed. These deviations in most cases result Bayer AG, Leverkusen, Degussa AG, Hanau, Hoechst from few data points at high molalities of carbon dioxide AG, Frankfurt, Linde KCA, Dresden, and Lurgi AG, where the increase in the total pressure curve is rather Frankfurt, is gratefully acknowledged. steep. Those pressures are determined by the amount of neutrally dissolved carbon dioxide and that amount Nomenclature is small in comparison to the overall amount of dissolved carbon dioxide, i.e., in either ionic or neutral form. To A+ = Debye-Huckel parameter further illustrate this, Figure 11shows predicted “true” Al,w...El,w = coefficients for the temperature dependence of molalities of all species (except Hf and OH-) present Henry’s constants in the liquid phase for a solution with f i = 4~mol/kg ~ ~ AR ... DR = coefficients for the temperature dependence of at 313.15 K. Furthermore, the number of moles of solid equilibrium constants N a H C O h g of water is shown. As it was expected, A, ...D, = coefficients for the temperature dependence of adding carbon dioxide t o an ammoniacal solution resolubility products duces the neutral amount of ammonia, thereby producal...a6 = coefficients in Saul and Wagner’s equation for the ing ammonium, carbamate, bicarbonate, and carbonate vapor pressure of pure water ions. When the solubility limit of NaHC03 is reached, a,,r...d,,,= coefficients for the temperature dependence of the increase in the concentration of HCO3- is damped. second virial coefficients Especially interesting is the behavior of the carbon a, = activity of component i dioxide concentration: At first glance, one would asB(0) G,MX = “observable” combination of binary interaction sume that this concentration can be neglected at all. parameters For example for a solution containing an overall amount B,, = second virial coefficient for interactions between of carbon dioxide of 4 mol/kg, the predicted amount of species i and j neutral carbon dioxide is 0.144 mol/kg, i.e., 96.4% of b = constant in modified Debye-Huckel expression carbon dioxide is present either in ionic form or as solid bl ...b6 = coefficients in Saul and Wagner’s equation for the NaHC03 rather than in neutral form. The predicted density of pure water total pressure above that solution is 1.124 MPa, the C@= third virial coefficient in Pitzer’s equation partial pressure of carbon dioxide is 1.117MPa. Thus, D = relative dielectric constant of water 3.6% of the overall molality of carbon dioxide cause 99.4% of the total pressure above the solution. This e = charge of proton
1468 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 f = functions for the temperature dependence of interaction
parameters f i , fz, f3 = functions in Pitzer’s equation GE = excess Gibbs energy I-$;) = Henry‘s constant for the solubility of gas i in pure water (on molality scale) h, = enthalpy of component i I = ionic strength (on molality scale) KR = equilibrium constant for chemical reaction R (on molality scale) KM,+X,-.~,H~O = solubility constant for the formation of solid species M,+X,-Y,H~O (on molality scale) k = Boltzmann constant Mu = molar mass of water in kg/mol f i l = overall molality of component i m, = true molality of component i NA = Avogadro’s number Np = number of phases ii, = overall number of moles of component i n, = true number of moles of component i p = total pressure p L= partial pressure of component i q, = coefficients for the temperature dependence of interaction parameters R = universal gas constant t = Celsius temperature T = absolute temperature U,= coefficients for the temperature dependence of the dielectric constant of pure water u = partial molar volume y = mole fraction in vapor z, = number of charges of component i Greek Letters a = constant in modified Debye-Huckel expression P ( O ) , ,W) = binary interaction parameters in Pitzer’s equation rG,MX,MX, rG,G,MX = “observable” combination of ternary interaction parameters y* = activity coefficient normalized to infinite dilution (on molality scale) EO = vacuum permittivity 6 = reduced temperature in the equations by Saul and Wagner ,IlJ= second virial coefficient in Pitzer’s equation p, = chemical potential of component i V,,R = stoichiometric coefficient of component i in reaction R vc, v- = number of cations and anions in salt MX e = mass density t = ternary interaction parameter in Pitzer’s equation rpl = Giauqe function of component i p = fugacity coefficient Subscripts c = critical f = formation G = gas G i , j , k = component i, j , k MX = salt MX M = cation M X = anion X max = maximum min = minimum R = reaction R or reference w = water Superscripts m = on molality scale s = saturation * = normalized to infinite dilution = infinite dilution ’ = solid phase
-
“
= liquid phase
”’ = gas phase
0 = reference state
Appendix 1. Brief Outline of Pitzer’s Model Pitzer’s (1973) equation for the excess Gibbs energy of an aqueous, salt-containing system is
i*w j t w k t w
The function
f~(n is a modified Debye-Huckel
fl(I) = -A,(U/b)ln(l
+b h )
term:
(33)
where I is the ionic strength: 2 I = l/zCmizi
(34)
1
and b = 1.2 (kg/mol)1’2. A, is the Debye-Huckel parameter for the osmotic coefficient:
&,(I) is the ionic strength dependent second virial coefficient:
AiJ(I)= p y
/?is’
+ p:y2(x)
(36)
:I?/
where and are binary interaction parameters. The function f2 is defined as
+
f 2 ( x )= (2/x2)(1- (1 x)e-”>
(37)
where x = a h . For the salts considered here, a = 2.0 (kg/mol)1’2. Differentiation of eq 32 yields the activity coefficient of the dissolved species i:
JI
j t w k*w
2
j t w k*w
where f3 is defined as
The activity of water follows from the Gibbs-Duhem equation
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1459
For systems containing a single salt M,+X,-, the binary and ternary parameters involving two or more species of the same sign of charge are usually neglected. The ternary parameters ZM,X,X and ZM,M,X are usually reported as third virial coefficients C@for the osmotic coefficient. Instead of rewriting eqs 38 and 40 in terms of (3,we preferred to set ZM,X,X to zero and calculated the ternary parameters ZM,M,X from numbers reported for C+:
Appendix 2. Interaction Parameters for Pitzer's Equation The following section reports relations for the temperature dependence of ion interaction parameters. T is the temperature in kelvin and TR= 298.15 K. NazS04: Ion interaction parameters, Rogers and Pitzer (1981) (298.15 rT/K 5 473.15):
0.01869 1.0994 0.005549 0.002349 0.005958 -0.000479 -1.036113-5 3.002993-2 - 1.43441El
48 49
4 10 411 412
q13 q14
415
-6.668943- 1 -3.235503-4 5.76552E-1 - 1.8876932 -2.05974B-1 1.46744E3 5.14316E-5 3.45791E-1
(NH4)2S04: Ion interaction parameters, Rumpf and Maurer (1993a) (313.15 I T/K I 383.15):
fln= 41 + 42/T parameter P%,-,SO,S-
PNH,-,S0,2 (11 -
C@
42
TmmK
-9.342 -2479 -1.070
313.15
41
0.1170 7.488 -1.2372 x
TmJK 383.15
NaHC03, Na2C03: Ion interaction parameters, Peiper and Pitzer (1982) (273 5 2°K 5 323). AT) = 41
48(T -l263 - T R -l 263) (43)
+ 42(T - T R ) + 43(T - TR)2
salt
parameter
41
NaHC03
pol
0.028 0.044 0.0362 1.51 5.2 10-3
pc1,
Na2C03
pol pel) C@
1 0 3 ~ ~ 1oq3 1.0 1.1 1.79 2.05
-1.3 -2.15 -2.11 -8.4
Appendix 3. Dielectric Constant of Pure Water The relative dielectric constant of water is (Bradley and Pitzer, 1979)
+ U32? +
D(T,p) = U,exp(U2T
+
)
C(T)ln(B(T) B ( T ) 1000 +p (49)
1
1
1
)
q12(T- 263 - T R - 263 - 680q13((T- 680)T (TR
where
- 680)TR
u1 uz u3 u 4 u 5
3,427932 -5.08663-3 9.46903- 7 -2.0525 3.115933
U6
U7
ua u 9
-1,828932 -8.032533 4.214236 2.1417
In these equations, p is in bars. Note: In the range investigated here, p was set equal to the saturation pressure of pure water.
Appendix 4. Equations for the Vapor Pressure of Pure pk and Saturated Liquid Density Water Equations by Saul and Wagner (1987):
1460 Ind. Eng. Chem. Res., Vol. 34,No. 4,1995
E) :
In - = -(a,O
and sodium sulfate at temperatures between 313 and 393 K (6 pages). Ordering information is given on any current masthead page.
+ a303+ a403.5+ a504+
+
Literature Cited
(53)
b@43'3 + b,0110/3
where
0 = 1 - TIT, a1 a2 a3 a4
a5 a6
-7.85823 1.83991 -11.7811 22.6705 - 15.9393 1.77516
bi bz b3 b4 b5 b6
(54) 1.99206 1.10123 -0.512506 - 1.75263 -45.4485 -6.75615E5
Critical properties of water: p , = 22.064 MPa, T, = 647.14 K, e, = 322.0 kg/m3.
Appendix 5. Solubility Product for the Formation of NaHC03 Brewer (1982)reports values for the Giauqe functions = -@pAT) - hPk298.15 K))/(RT) and standard enthalpies of formation h!k298.15 K) for various substances. Standard thermodynamics yields the solubility product for the formation of solid NaHC03: r$i
In KNaHCO, = -&~Hco, + &a+ + +HCO,- + h:aHc09,A298.15 K) - hLa+,d298.15 K) - h&0R-,-(298.15K) RT (55) The following values as taken from Brewer were used:
+ 1.371 x 10-4t2 5.136 x 10-7t3+ 5.68 x 10-1°t4 (56) 4HC0,-= 11.90 - 2.96 1 0 - ~ + t 3.09 1 0 - ~ t~ 2.52 + 5.4 10-I0t4 (57) 4NaHC03 - 15.17 - 1.985 x 10-'T + 3.46 x 1 0 - 5 p '
= 7.21 - 9.53 x 10-3t
(58)
The values for h!A298.15 K)/R: h:aHc03,f(298.15 K)/R = -114 130 K
(59)
h:,+,k298.15 K)IR = -28 912 K
(60)
SupplementaryMaterial Available: Tables 8-10 with additional experimental data for the total pressure above aqueous solutions of ammonia, carbon dioxide,
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Received for review August 23, 1994 Revised manuscript received December 28, 1994 Accepted J a n u a r y 4, 1995@ IE940511S Abstract published i n Advance A C S Abstracts, March 1, 1995. @
