Presure-Volume-Temperature Properties of H2O-CO2 Fluids (Geophysics) [Short Article] - T. Bowers...

Pressure-Volume-Temperature Properties of H,O-CO, Fluids

Teresa S. Bowers

1. INTRODUCTION

Pressure-volume-temperature properties of water and carbon dioxide have been accurately measured for decades, and equations of state (EOS) describing the relationship between these properties have been suggested for nearly as long. Most of the information found in the chapter by Kennedy and Holser in the 1969 Handbook of Physical and Chemical Constants is as correct today as it was then. However, considerable new information has recently be- come available concerning such things as the properties of water in the near-critical region, the effect of carbon dioxide on the dielectric constant of water, and very high pressure volumes of water and carbon dioxide achieved through shock compression.

Data prescribing the pressure-volume-temperature properties of water, carbon dioxide and water-carbon dioxide mixtures are tabulated herein. Related properties, including enthalpy, entropy, heat capacity, sound speed, and the dielectric constant, that can be derived through EOS are tabulated as well. A description of each property is given, and the relevance of each property to the understanding of geophysical or geochemical problems is briefly described. The relationship of each property to other properties, and sources of data or tabulated values are also given. Where data sources provide data for overlapping conditions, the sources are used preferentially in the order that they are listed. Experimental data are given in bold type in all tables. Smoothed or interpolated values are given in reg-

T. S. Bowers, Gradient Corporation, 44 Brattle Street, Cam- bridge, MA 02138

Rock Physics and Phase Relations A Handbook of Physical Constants AGU Reference Shelf 3

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Copyright 1995 by the American Geophysical Union. 45

ular type, while information calculated from an EOS is given in italics. The use of data from multiple sources pro- duces some discontinuities in the tabulated information.

The second section provides information on EOS. A variety of EOS exist for water, carbon dioxide, and water- carbon dioxide mixtures, and are used to calculate values of properties in the absence of measurements, and to derive derivative or integral properties.

2. WATER

2.1 Volume Volume, or density, is usually measured. All other prop-

erties can be related by derivatives or integrals to volume. Detailed measurements of the volume of water at elevated pressures and temperatures have been made by (8) and (25). Water volumes are tabulated here in Table la-d from 0” to 2000°C and 1 bar to 250 Kbar based on data and tabula- tions of (15), (10) and (33). The work of (15) is based on a variety of measurements, including those of (25). Table 2 gives water densities at higher pressures and temperatures obtained from shock experiments by (24) and (28). Addi- tional shock experiment data can be found in (1) and (3).

2.2 Thermodynamic Functions The thermodynamic properties presented here for water

are taken from Haar et al. (15). Haar et al. use an equation of state for water that represents its properties by a molar Helmholtz energy function, A, which is written in terms of temperature (7) and density (p). Other thermodynamic properties can be derived from the appropriate derivatives of the Helmholtz function. Those presented here include entropy (s), enthalpy (E-T), and heat capacity at constant pressure CC,,). Expressions relating these properties to the Helmholz function and to each other are given in Table 3.

46 H,O-CO, FLUIDS

TABLE la. Water Volume, cm3/mole Pbars/T’C 0 20 40 60 80 100 120 140 160 1 18.0191 18.0479 18.1574 18.3239 18.5385 30557. 32304. 34030. 35 740. 10 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 12000 14000 16000 18000 20000

18.0108 17.9971 17.9744 17.9297 17.8857 I 7.8425 I 7.7998 17.7580 17.7168 17.6762 17.5969 I 7.5200 I 7.4454 17.3732 17.3031 17.2352 17.106 16.984 16.870 16.764 16.665 16.569 16.481 16.398 16.319 16.243 16.171 16.103 16.036 15.973 15.912 15.766 15.631

18.0405 18.0281 18.0077 17.9674 17.9275 17.8883 17.8497 17.8115 17.7740 17.7371 17.6645 17.5941 I 7.5252 17.4584 17.3934 17.3298 17.207 I 7.092 16.982 16.877 16.776 16.683 16.591 16.504 16.422 16.342 16.267 16.193 16.121 16.052 15.984 15.832 15.669 15.519 15.375 15.234

18.1502 18. I381 18.1183 18.0791 18.0405 18.0023 17.9648 17.9279 17.8915 17.8555 17.7850 17.7166 17.6497 17.5847 17.5213 17.4593 17.340 I 7.225 17.117 17.013 16.913 16.818 16.728 16.640 16.555 16.474 16.396 16.321 16.249 16.178 16.110 15.946 15.793 15.645 15.505 15.369 15.240 15.115 14.998 14.890

18.3165 18.3043 18.2843 18.2443 18.2052 18.1666 18.1286 18.0911 18.0544 18.0180 17.9470 17.8778 17.8106 I 7.7450 17.6813 17.6189 17.499 I 7.384 17.274 17.169 17.068 16.973 16.879 16.791 16.704 16.622 16.542 16.467 16.391 16.321 16.250 16.085 15.932 15.787 15.652 15.524 15.402 15.287 15.177 15.072 14.973 14.879 14.793

18.5307 18.5179 18.4968 18.4551 18.4142 18.3738 18.3343 18.2952 18.2571 18.2192 18.1455 18.0738 18.0043 17.9367 17.8708 17.8067 I 7.683 I 7.566 I 7.452 17.346 17.241 17.142 17.049 16.957 16.868 16.784 16.701 16.622 16.546 16.472 16.400 16.231 16.074 15.926 15.789 15.660 15.539 15.423 15.314 15.211 15.114 15.020 14.932 14.620

18.7898 18.7761 18.7534 18.7085 18.6648 18.6215 18.5794 18.5377 18.4968 18.4569 18.3785 18.3028 18.2293 18.1580 18.0888 18.0214 17.892 17.769 17.652 17.540 I 7.432 17.330 17.231 17.137 17.045 16.957 16.872 16.789 16.710 16.634 16.559 16.384 16.220 16.067 15.924 15.791 15.665 15.546 15.434 15.326 15.225 15.130 15.038 14.712 14.436

19.0937 19.0786 19.0535 19.0044 18.9563 18.9092 18.8631 18.8179 18.7736 I8.7302 18.6455 18.5639 18.4848 18.4084 18.3343 18.2625 18.124 I 7.994 17.870 17.753 17.639 17.531 17.429 17.330 17.234 17.142 17.054 16.967 16.885 16.805 16.728 16.544 16.373 16.214 16.065 15.924 15.793 15.669 15.551 15.440 15.333 15.233 15.137 14.791 14.499 14.247

19.4447 19.4276 19.3994 19.3445 19.2906 19.2383 19.1870 19.1370 19.0880 19.0400 18.9469 18.8575 18.7714 18.6882 18.6078 18.5302 18.382 18.241 18.110 17.984 17.865 I 7.749 17.641 17.537 17.436 I 7.339 I 7.245 17,157 17.068 16.985 16.904 16.712 16.533 16.368 16.213 16.065 15.928 15.798 15.674 15.557 15.447 15.341 15.240 14.876 14.566 14.297 14.060

19.8473 19.8277 19.7956 19.7326 19.672 19.612 19.555 19.497 19.443 19.389 19.284 19.185 19.090 18.998 18.910 18.825 18.663 18.511 18.369 18.234 18.106 17.984 I 7.868 17.757 17.650 17.548 17.448 17.355 17.263 17.175 17.090 16.888 16.701 16.526 16.364 16.211 16.067 15.932 15.804 15.681 15.564 15.454 15.348 14.966 14.640 14.357 14.107 13.883

BOWERS 47

TABLE lb. Water Volume, cm3/mole Pbars/TOC 180 200 220 240 260 280 300 320 340

37443. 39136. 40822. 42507. 44188. 45865. 47541. 49214. 50886. 1 10 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4500 5000 5500 6000 6500 7000 75ocl 8000 8500 9000 9500 10000 12000 14000 16000 18000

3502.9 20.2867 20.2491 20.1758 20.104 20.036 19.969 19.904 19.841 19.780 19.663 19.551 19.443 19.342 19.243 19.149 18.971 18.805 18.650 18.504 18.366 18.234 18.110 17.991 17.877 17.767 17.663 17.562 17.467 17.373 17.283 17.070 16.874 16.692 16.521 16.362 16.211 16.068 15.935 15.807 15.687 15.569 15.460 15.061 14.721 14.425 14.162

3709.5 20.8166 20.7712 20.6834 20.599 20.518 20.439 20.363 20.291 20.219 20.084 19.956 19.836 19.720 19.609 19.504 19.306 19.122 18.953 18.792 18.643 18.501 18.366 18.238 18.115 18.000 17.888 17.782 17.679 17.580 17.485 17.259 17.054 16.861 16.683 16.515 16.359 16.211 16.070 15.937 15.811 15.690 15.575 15.160 14.806 14.497 14.224

3906.9 4097.7 4284.0 4466.7 4646.9 4824.9 5001.2 21.4349 1520.0 1612.3 1698.7 1781.4 1861.2 1939.1 21.3789 22.0982 22.9727 760.82 816.20 866.41 913.21 21.2711 21.9611 22.7899 23.8202 25.1766 346.77 386.70 21.169 21.832 22.621 23.587 24.821 26.529 29.379 21.070 21.711 22.464 23.374 24.511 26.019 28.258 20.976 21.594 22.316 23.179 24.237 25.597 27.485 20.886 21.484 22.179 22.999 23.992 25.237 26.889 20.799 21.380 22.048 22.832 23.769 24.920 26.401 20.717 21.279 21.925 22.675 23.563 24.639 25.986 20.558 21.090 21.695 22.390 23.197 24.152 25.305 20.409 20.915 21.486 22.134 22.877 23.740 24.759 20.270 20.753 21.293 21.902 22.592 23.383 24.300 20.136 20.599 21.115 21.689 22.334 23.068 23.904 20.012 20.455 20.947 21.493 22.100 22.783 23.556 19.893 20.320 20.790 21.309 21.886 22.527 23.244 19.672 20.068 20.502 20.978 21.500 22.073 22.707 19.466 19.839 20.245 20.684 21.162 21.682 22.253 19.279 19.630 20.009 20.419 20.861 21.340 21.859 19.102 19.436 19.794 20.178 20.590 21.034 21.511 18.938 19.256 19.594 19.956 20.342 20.756 21.201 18.783 19.086 19.409 19.751 20.115 20.504 20.918 18.638 18.928 19.234 19.560 19.906 20.272 20.661 18.501 18.778 19.072 19.382 19.710 20.057 20.425 18.369 18.636 18.917 19.214 19.528 19.857 20.205 18.243 18.501 18.771 19.056 19.355 19.670 20.001 18.124 18.373 18.632 18.906 19.192 19.493 19.810 18.011 18.250 18.501 18.764 19.039 19.328 19.630 17.901 18.133 18.375 18.629 18.893 19.171 19.461 17.794 18.020 18.256 18.501 18.755 19.021 19.301 17.694 17.913 18.140 18.376 18.623 18.881 19.147 I 7.4S6 I 7.661 17.872 18.090 18.317 18.553 18.798 17.238 17.429 17.627 17.830 18.041 18.259 18.484 17.036 17.216 17.402 17.593 17.789 I 7.993 18.202 16.849 17.020 17.194 17.373 17.558 17.748 17.942 16.674 16.836 17.000 17.171 17.344 17.522 17.704 16.510 16.663 16.820 16.980 17.144 17.313 17.485 16.355 16.501 16.650 16.804 16.958 17.117 17.279 16.207 16.348 16.490 16.636 16.784 16.935 17.088 16.068 16.204 16.339 16.477 16.620 16.762 16.908 15.937 16.067 16.196 16.330 16.463 16.600 16.739 15.811 15.935 16.061 16.187 16.315 16.447 16.578 15.692 15.811 15.932 16.052 16.175 16.301 16.427 15.261 15.364 15.467 15.571 15.676 15.782 15.888 14.894 14.982 15.072 15.162 15.252 15.344 15.434 14.573 14.651 14.728 14.807 14.887 14.966 15.045 14.288 14.357 14.425 14.494 14.564 14.633 14.703

48 H,O-CO2 FLUIDS

TABLE lb. (continued) Pbars/T”C 180 200 220 240 260 280 300 320 340 20000 13.928 13.979 14.034 14.094 14.153 14.215 14.276 14.337 14.398 25000 13.46 13.49 13.55 13.58 13.62 13.67 13.71 13.76 30000 13.12 13.15 13.19 13.22 13.26 40000 12.46 12.70 50000 12.20 60000 11.84 70000 11.54 80000 90000 100000 10.36 150000 9.26 200000 8.61 250000 8.18

Values calculated by (15), (10) and (33).

TABLE lc. Water Volume, cm3/mole Pbars/T”C 360 380 400 420 440 460 480 500 600 1 52558. 54228. 55898. 57567. 59235. 60903. 62570. 64236. 72567. 10 5176.4 5350.4 5523.3 5695.8 5867.5 6038.6 6209.2 6379.5 7226.0 25 2015.1 2089.9 2163.5 2236.5 2308.6 2380.1 2451.3 2521.7 2869.9 50 957.6 1000.2 1041.5 1081.7 1121.0 1159.7 1197.7 1235.2 1417.7 100 419.77 449.01 475.77 500.79 524.52 547.29 569.27 590.64 691.11 150 226.48 257.18 281.99 303.61 323.17 341.33 358.43 374.73 448.67 200 32.876 148.74 179.19 201.60 220.34 236.89 252.01 266.08 32 7.33 250 30.564 40.033 108.11 136.56 156.60 173.04 187.40 200.39 254.49 300 29.310 33.740 50.32 88.62 112.20 129.52 143.80 156.31 205.94 350 28.436 31.600 37.936 55.352 79.50 97.92 112.44 124.74 171.35 400 2 7.761 30.290 34.403 42.509 52.729 74.77 89.14 101.23 145.52 500 26.745 28.609 31.169 34.937 40.799 49.436 59.81 70.12 109.86 600 25.984 2 7.496 29.417 31.944 35.374 40.064 46.146 53.232 86.95 700 25.376 26.662 28.226 30.164 32.614 35.737 39.668 44.400 71.56 800 24.869 25.995 27.327 28.919 30.847 33.191 36.036 39.423 60.98 900 24.435 25.442 26.610 27.972 29.571 31.460 33.686 36.284 53.54 1000 24.053 24.968 26.013 27.210 28.586 30.175 32.007 34.108 48.180 1200 23.408 24.188 25.058 26.030 27.118 28.337 29.703 31.227 41.219 1400 22.877 23.560 24.311 25.136 26.046 27.044 28. I43 29.344 36.987 1600 22.423 23.033 23.698 24.419 25.204 26.057 26.981 27.979 34.151 1800 22.026 22.581 23.178 23.823 24.516 25.262 26.064 26.921 32.103 2000 21.675 22.185 22.729 23.311 23.934 24.601 25.311 26.066 30.537 2200 21.360 21.832 22.333 22.866 23.433 24.035 24.675 25.350 29.290 2400 21.075 21.513 21.978 22.471 22.992 23.543 24. I25 24.738 28.267 2600 20.814 21.225 21.659 22.116 22.599 23.109 23.642 24.204 2 7.402 2800 20.572 20.960 21.367 21.796 22.246 22.718 23.214 23.732 26.660 3000 20.349 20.715 21.099 21.502 21.924 22.367 22.828 23.311 26.013 3200 20.140 20.488 20.852 21.232 21.630 22.044 22.479 22.929 25.440 3400 19.946 20.277 20.621 20.981 21.358 21.751 22.158 2.581 24.927 3600 19.762 20.077 20.407 20.749 21.106 21.477 21.862 22.262 24.464 3800 19.589 19.891 20.205 20.531 20.872 21.225 21.589 21.967 24.044 4000 19.425 19.715 20.016 20.327 20.652 20.987 21.335 21.695 23.659 4500 19.050 19.313 19.585 19.87 20.16 20.47 20.77 21.08 22.83 5000 18.717 18.958 19.205 19.46 19.73 20.00 20.29 20.57 22.12

BOWERS 49

TABLE lc. (continued)

Pbars/T°C 360 380 400 420 440 460 480 500 600

5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 12000 14000 16000 18000 20000 25000 30000 40000 50000 60000 70000 80000 90000 100000 150000 200000 250000

18.416 18.638 18.142 18.349 I 7.892 18.084 17.661 17.841 I 7.445 17.614 I 7.245 17.405 I 7.056 17.207 16.879 I 7.023 16.713 16.849 16.555 16.685 15.996 16.105 15.528 15.620 15.124 15.206 14.773 14.842 14.460 14.521 13.80 13.85 13.28 13.31

18.866 18.560 18.281 18.025 17.787 17.567 I 7.362 17.169 16.987 16.816 16.214 15.714 15.285 14.912 14.582 13.89 13.35 12.96 12.41 12.01 11.68 11.35 10.92 10.35 9.42 8.70 8.27

19.10 19.35 19.58 19.85 18.77 19.01 19.22 19.46 18.48 18.68 18.90 19.11 18.21 18.41 18.61 18.81 17.966 18.146 18.329 18.519 17.735 17.904 18.077 18.254 17.519 17.679 I 7.843 18.009 17.319 17.470 17.623 17.780 17.130 17.272 17.418 17.567 16.951 17.086 17.225 I 7.366 16.326 16.440 16.553 16.668 15.807 15.903 16.000 16.097 15.366 15.449 15.532 15.614 14.984 15.054 15.124 15.196 14.645 14.706 14.768 14.831 13.94 13.98 14.03 14.07 13.39 13.42 13.46 13.49

20.11 21.51 19.71 20.99 19.35 20.52 19.01 20.11 18.710 19.73 18.434 19.39 18.178 19.06 I 7.940 18.77 17.719 18.502 17.510 18.259 16.786 I 7.394 16.195 16.703 15.697 16.128 15.269 15.638 14.894 15.213 14.12 14.36 13.51 13.69 13.23 13.51 12.62 12.84 12.18 12.36 II.83 11.98 11.49 11.63 11.07 11.22 10.53 10.71 9.57 8.81 8.34

Values calculated by (15), (10) and (33).

TABLE Id. Water Volume, cm3/mole Pbars/T’C 700 800 900 1000 1200 1400 1600 1800 2000 1 80892. 89213. 97540. 105860. 122490. 139120. 155750. 172380. 189020. 10 8067.7 8906.4 9743. 10579. 12247. 13916. 15580. 17245. 18910. 25 3212.8 3552.8 3890.7 4227.5 4898.6 5567.8 6235.9 6903.2 7570.0 50 1594.4 1768.3 1940.0 2110.6 2449. I 2785.6 3121.1 3455.6 3790.0 100 785.32 876.12 964.8 1052.1 1224.4 1394.6 1563.8 1732.2 1900.0 150 515.6 578.9 639.9 699.6 816.5 931.2 1044.7 1157.7 1270.1 200 380.73 430.28 477.57 523.42 612.5 699.6 785.3 870.5 955.2 250 299.86 341.19 380.21 417.76 490.2 560.7 629.8 698.3 766.4 300 246.01 281.86 315.35 347.37 408.8 468.1 526.1 583.5 640.5 350 207.60 239.52 269.07 297.10 350.6 401.9 452.0 501.4 550.4 400 I 78.90 207.83 234.39 259.45 306.8 352.2 396.5 440.0 483.0 500 138.96 163.64 182.96 206.81 245.9 282.9 318.7 353.8 388.6 600 112.76 134.42 153.82 171.80 205.2 236.6 267.0 296.5 325.5 700 94.49 113.81 131.01 146.88 176.2 203.6 229.9 255.5 280.7 800 81.25 98.60 114.08 128.31 154.51 178.86 202.14 224.75 246.93 900 71.36 87.02 101.05 113.97 137.66 159.64 180.56 200.82 220.68 1000 63.81 77.97 90.78 102.58 124.24 144.25 163.30 181.69 199.67 1200 53.27 64.97 75.76 85.79 104.24 121.27 137.41 152.97 168.14 1400 46.50 56.21 65.42 74.08 90. IO 104.93 118.96 132.49 145.62 1600 41.85 50.03 57.98 65.54 79.65 92.76 105.18 117.12 128.74 1800 38.52 45.47 52.41 59.07 71.65 83.36 94.49 105.21 115.61

50 H,O-CO, FLUIDS

TABLE Id. (continued) Pbars/T"C 700 800 900 1000 1200 1400 1600 1800 2000

2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 12000 14000 16000 18000 20000 25000 30000 40000 50000 60000 70000 80000 90000 100000 150000 200000 250000

36.01 42.03 34.05 39.33 32.48 37.15 31.19 35.37 30.09 33.87 29.15 32.61 28.34 31.51 27.62 30.56 26.97 29.71 26.39 28.95 25.87 28.27 24.75 26.83 23.84 25.67 23.06 24.70 22.39 23.89 21.80 23.17 21.29 22.54 20.83 21.98 20.41 21.49 20.02 21.02 19.67 20.63 19.35 20.25 19.06 19.89 18.041 18.72 17.240 17.800 16.580 17.052 16.025 16.427 15.546 15.894 14.59 14.83 13.85 14.03 13.79 14.07 13.06 13.28 12.54 12.72 12.14 12.29 11.78 11.92 11.38 11.53 10.89 11.06

48.12 44.72 41.98 39.73 37.83 36.23 34.84 33.64 32.57 31.64 30.79 29.02 27.60 26.43 25.44 24.59 23.85 23.19 22.61 22.09 21.60 21.17 20.75 19.42 18.382 17.544 16.847 16.254 15.08 14.21

54.05 50.05 46.79 44.09 41.83 39.91 38.23 36.79 35.51 34.37 33.37 31.26 29.56 28.20 27.04 26.05 25.19 24.43 23.76 23.15 22.61 22.11 21.66 20.14 18.982 18.050 17.281 16.629 15.35 14.39 15.11 14.40 13.76 13.21 12.71 12.27 11.85 10.32 9.35 8.71

65.34 75.92 85.99 95.70 105.12 60.26 69.88 79.07 87.94 96.57 56.08 64.91 73.34 81.50 89.43 52.61 60.73 68.53 76.06 83.41 49.67 57.18 64.43 71.43 78.26 47.15 54.14 60.89 67.43 73.83 44.97 51.49 57.81 63.94 69.94 43.06 49.18 55.11 60.88 66.52 41.38 47.13 52.71 58.16 63.49 39.91 45.31 50.59 55.74 60.79 38.57 43.69 48.68 53.56 58.35 35.78 40.27 44.68 49.00 53.26 33.58 37.56 41.49 45.36 49.18 31.78 35.37 38.90 42.41 45.85 30.28 33.53 36.75 39.94 43.09 29.01 31.98 34.93 37.85 40.75 27.91 30.65 33.37 36.07 38.73 26.95 29.47 32.00 34.50 37.00 26.09 28.45 30.81 33.15 35.47 25.33 27.55 29.74 31.92 34.12 24.66 26.72 28.79 30.84 32.90 24.03 25.98 27.92 29.87 31.82 23.47 25.31 27.15 28.99 30.83 21.62 23.11 24.63 26.14 27.67 20.21 21.48 22.75 24.03 25.33 19.10 20.18 21.28 22.39 23.51 18.18 19.11 20.09 21.06 22.05 17.412 18.234 19.084 19.953 20.837 15.91 16.52 17.15 17.82 18.52 14.81 15.26 15.76 16.27 16.83

BOWERS 51

TABLE 2. Shock-Compressed Water Data Temperature Pressure Density

(Kb) Wm3) 09 - 292. 2.05 2067. 316. 2.08 2067. 383. 2.16 2533. 489. rfr 9. 2.26 + 0.01 3280. 585. + 11. 2.34 + 0.01 3830. 619. &- 12. 2.36 f 0.01 4090. 710. f 30. 2.41 + 0.02 4480. 800. + 18. 2.47 + 0.01 5270.

Values from (24) and (28).

TABLE 3. Thermodynamic Functions

Entropy @‘I s,A

aT

Enthalpy (H) H=U+f

P

2 aA P-p - aP

lJ=A+TS

Heat Capacity (C,)

ap 2 #A aTEP apaT

Gibbs Free Energy (G) G=A+:

P

Gibbs Free Energy (G), which is not tabulated here or in Haar et al., can be derived from the relationship for G given in Table 3, or from rearrangement of those equations, by G = H - TS. G can then be calculated from values for H and S given in Tables 4 and 5.

Enthalpies, entropies, and heat capacities are tabulated from 0” to 2000°C and 1 bar to 30 Kbar in Tables 4a-c, Sa-c, and 6a-c, respectively. Properties of water along the coexistence curve for liquid and vapor are compiled in Table 7. This table includes the pressure and temperature of coexistence, and the volumes, enthalpies and entropies of the coexisting phases. Values given in Tables 4 through 7 are taken from (15). Additional thermodynamic properties as well as additional pressure-temperature intervals for the properties can be found in (15).

An alternate form of the thermodynamic properties called the apparent properties are given by (16) and (19), among others. The conversion from the values of enthalpy and entropy listed here to values of apparent molal enthalpies and entropies requires the addition of triple point values of H and S, respectively. This conversion is described in detail, and triple point values necessary to make the conversions are given on page 568 of (19).

2.3 Sound Speed The speed of sound in water can be derived from an

EOS. Mathematical relationships are presented in (15), (19) and (23). Sound speeds are given in Table Sa-c from 0” to 2000°C and 1 bar to 30 Kbar. Values are obtained from (15). (23) describes the effects that two phase fluid mixtures of water and another component can have on sound speed, and presents equations and graphs showing sound speeds in mixtures of water, steam and air.

2.4 Dielectric Constant The dielectric constant (E) of a fluid is a complex function

of pressure and temperature that provides a measure of the fluid’s electrostatic permittivity. It is useful in assessing electrostatic interactions in a fluid. The dielectric constant controls the extent of ion association that takes place in a solution, and hence, affects mineral solubilities. Isopleths of the dielectric constant are often used to predict the values of association constants for aqueous species outside the pressure and temperature range for which they have been measured. Values of the dielectric constant are compiled in Table 9a-c from 0” to 1000°C and 1 bar to 10 Kbar, and are taken from (15) and (2).

52 H20-CO2 FLUIDS

TABLE 4a. Water Enthalpy, kJ/kg Pbars/T"C 0 20 40 60 80 100 120 140 160

0.06 83.93 167.59 251.22 334.97 2675.9 2716.3 2756.2 2795,s 1 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000

2.51 5.05 10.10 15.11 20.08 25.02 29.92 34.79 39.63 49.20 58.65 67.99 77.22 86.35 95.40 113.2 130.8 148.2 165.3 182.4 267.0 352.1 439.4

86.18 88.52 93.20 97.85 102.48 107.09 111.68 116.25 120.80 129.85 138.83 147.75 156.60 165.38 174.11 191.4 208.5 225.4 242.2 258.8 340.6 421.0 500.6 579.4

169.71 171.92 176.33 180.74 185.13 189.50 193.87 198.23 202.57 211.23 219.84 228.41 236.94 245.43 253.88 270.7 287.3 303.8 320.2 336.5 416.6 495.0 571.7 646.1 717.4 785.5

253.24 336.88 420.87 505.40 590.63 255.34 338.87 422.75 507.16 592.26 259.53 342.85 426.52 510.70 595.53 263.72 346.84 430.29 514.24 598.83 267.90 350.82 434.07 517.81 602.15 272.08 354.80 437.85 521.38 605.49 276.25 358.79 441.64 524.96 608.85 280.41 362.77 445.44 528.56 612.22 284.57 366.75 449.24 532.16 615.61 292.88 374.71 456.84 539.40 622.44 301.16 382.66 464.46 546.66 629.32 309.41 390.60 472.09 553.96 636.25 317.64 398.54 479.72 561.27 643.23 325.85 406.46 487.36 568.61 650.24 334.03 414.38 495.00 575.96 657.28 350.3 430.2 510.3 590.7 671.5 366.5 445.9 525.6 605.5 685.7 382.6 461.6 540.8 620.3 700.1 398.7 477.3 556.1 635.2 714.5 414.6 492.9 571.3 650.0 729.0 493.4 570.2 647.2 724.4 801.8 570.7 646.5 722.4 798.5 874.8 646.8 722.1 797.2 872.4 947.8 721.5 796.9 871.5 946.0 1020.7 794.4 871.0 945.5 1019.4 1093.4 865.2 944.2 1019.2 1092.6 1166.1 934.0 1016.6 1092.7 1165.8 1238.6 1001.4 1088.2 1165.9 1238.9 1311.1

676.75 678.22 681.19 684.2 687.2 690.3 693.4 696.5 699.7 706.0 712.5 719.0 725.6 732.3 739.0 752.5 766.2 780.1 794.0 808.1 879.2 951.1 1023.3 1095.5 1167.7 1239.8 1311.8 1383.7 2104.

Values calculated by (15).

TABLE 4b. Water Enthalpy, kJ/kg PbarslT'C 180 200 220 240 260 280 300 350 400 1 2835.3 2874.8 2914.4 2954.0 2993.8 3033.8 3073.9 3175.3 3278.0 25 764.01 852.76 943.56 2850.8 2906.4 2958.4 3008.0 3125.8 3239.2 50 765.28 853.79 944.25 1037.40 1134.33 2855.9 2923.5 3067.7 3195.5 100 767.88 855.91 945.75 1038.03 1133.69 1234.23 1342.38 2922.2 3096.1 150 770.5 858.1 947.4 1038.9 1133.4 1232.2 1337.4 2691.3 2974.7 200 773.2 860.4 949.1 1039.9 1133.4 1230.7 1333.4 1645.4 2816.9 250 776.0 862.7 951.0 1041.1 1133.7 1229.7 1330.4 1623.1 2578.1 300 778.8 865.2 952.9 1042.4 1134.2 1229.0 1328.0 1608.1 2150.7 350 781.6 S67.6 954.9 1043.s 1134.9 1228.7 1326.1 1596.8 1988.3 400 784.5 870.1 957.0 1045.4 I135.7 1228.6 1324.8 15ss. 1 1930.8 500 790.3 875.3 961.4 1048.9 1137.9 1229.2 I323. I 1575.3 1874.1 600 796.2 880.7 966. I 1052.7 II40.7 1230.5 1322.6 1566.7 1843.0 700 802.3 886.2 971.0 1056.8 1143.8 1232.5 1323.0 1560.8 1822.8 800 SOS. 5 891.9 976.1 1061.1 1147.3 1234.9 1324.2 1556.9 1808.7 900 814.7 897.7 981.3 1065.7 1151.2 1237.8 1325.9 1554.4 1798.4 1000 821.1 903.6 986.7 1070.6 1155.3 1241.1 1328.2 1553.1 1790.9 1200 833.9 915.7 997.9 1080.7 1164.2 1248.6 1334.0 1781.5

BOWERS 53.

TABLE 4b. (continued) PbarslT’C 180 200 220 240 260 280 300 350 400 1400 847.0 928. I 1009.5 1091.4 1173.9 1257.1 1341.1 1777.2 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000

860.3 940.8 1021.5 1102.6 873.8 953.6 1033.8 1114.2 887.3 966.7 1046.3 1126.1 956.7 1034.2 1111.6 1189.1 1027.4 1103.6 1179.7 1255.6 1098.7 1174.0 1249.1 1324.1 1170.3 1245.0 1319.4 1393.6 1242.0 1316.2 1390.1 1463.8 1313.7 1387.4 1461.0 1534.3 1385.2 1458.7 1531.9 1604.9 1456.8 1529.9 1602.9 1675.7 2169. 2238. 2308. 2379.

1184.2 1266.3 1349.2 1776.3 1195.0 1276.2 1358.0 1777.8 1206.2 1286.7 1367.6 1781.2 1266.6 1344.3 1422. I 1815.2 1331.5 1407.4 1483.3 1864.5 1398.9 1473.5 1548.2 1921.4 1467.6 1541.4 1615.1 1982.8 1537.2 1610.4 1683.4 2047.0 1607.2 1680.0 1752.5 2113.0 1677.6 1750.0 1822.1 2180.2 1748. I 1820.3 1892.1 2248.4 2450. 2521. 2592. 2943. 3140. 3210. 3280. 3630.


TABLE 4c. Water Enthalpy, kJ/kg Pbars/T”C 500 600 700 800 900 1000 1200 1500 2000 1 3488.2 3705.0 3928.8 4159.7 4397.5 4642.0 5150.0 5953.3 7376.7 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000

3462.2 3433.9 3374.0 3309.3 3239.4 3164.2 3083.5 2997.3 2906.7 2724.2 2571.9 2466.9 2397.7 2350.3 2316.2 2271.4 2244.1 2227.0 2216.3 2210.0 2215.0 2249. I 2296. 2351. 2410. 2472. 2537. 2602. 3288. 3974.

3686.3 3666.2 3624.7 3581.5 3536.7 3490.4 3443.1 3394.7 3345.8 3247.7 3152.3 3063.8 2985.4 2918.7 2863.4 2781.1 2726.2 2688.8 2663.0 2645.0 2616.5 2634.2 2671. 2719. 2773. 2831. 2892. 2955. 3628. 4312.

3914.7 3899.7 3869.0 3837.6 3805.5 3773.0 3740.1 3706.9 3673.8 3607.8 3543.5 3481.9 3424.2 3371.1 3323.1 3242. 3179. 3132. 3096. 3069. 3012. 3015. 3043. 3084. 3134. 3188. 3246. 3306. 3966. 4646.

4148.6 4137.0 4113.5 4089.6 4065.4 4041.1 4016.7 3992.2 3967.8 3919.5 3872.3 3826.7 3783.3 3742.4 3704.3 3637. 3581. 3535. 3498. 3469. 3396. 3388. 3409. 3445. 3490. 3541. 3597. 3655. 4302. 4976.

4388.7 4379.4 4360.9 4342.2 4323.5 4304.7 4285.9 4267.2 4248.5 4211.5 4175.4 4140.3 4106.6 4074.6 4044.3 3989. 3942. 3902. 3868. 3841. 3764. 3750. 3767. 3799. 3842. 3891. 3944. 4001. 4636. 5303.

4634.9 5145.2 5950.6 7375.8 4627.4 5140.2 5947.7 7374.8 4612.5 5130.3 5942.2 7373.1 4597.7 5121. 5937. 7371. 4582.8 5111. 7370. 4568.0 5101. 7369. 4553.3 5092. 7367. 4538.5 5082. 7366. 4523.9 5073. 7365. 4495.0 5055. 7363. 4466.7 5037. 7361. 4439.1 5019. 7359. 4412.5 5002. 7357. 4386.9 4985. 7355. 4362.6 4970. 73.54. 4318. 4940. 7351. 4279. 4913. 7348. 4244. 4889. 7346. 4215. 4868. 7344. 4191. 4850. 7343. 4119. 4796. 7346. 4103. 4784. 7364. 4117. 4797. 7394. 4147. 4826. 7431. 4188. 4866. 7476. 4235. 4912. 7524. 4287. 4962. 7576. 4343. 5016. 7630. 4968. 5627. 8218. 5628. 6271. 8804.

54 H,O-CO, FLUIDS

TABLE 5a. Water Entropy, kJ/kg-K Pbars/T”C 0 20 40 60 80 100 120 140 160 1 -.00015 0.29619 0.57225 0.83115 1.07526 7.3609 7.4665 7.5655 7.6591 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000

0.00003 0.00020 0.00045 0.00060 0.00066 0.00063 0.00051 0.00031 0.00003 -.00076 -.00184 -.00318 -.00476 -.00655 -. 00854 -0.0130 -0.0180 -0.0233 -0.0287 -0.0342 -0.0587 -0.0736 -0.0744

0.29568 0.29514 0.29405 0.29292 0.29176 0.29057 0.28935 0.28810 0.28682 0.28419 0.28144 0.2 7860 0.27566 0.27264 0.26954 0.2631 0.2565 0.2497 0.2427 0.2357 0.2014 0.1699 0.1417 0.1166

OS7132 0.5 7034 0.56839 0.56644 0.56449 0.56253 0.56057 0.55861 0.55665 0.55270 0.54874 0.54477 0.54078 0.53678 0.53276 0.5247 0.5166 0.5084 0.5003 0.4922 0.4522 0.4139 0.3761 0.3364 0.2916 0.2412

0.82987 1.07369 1.30502 1.52568 1.73714 1.94068 0.82855 1.07205 1.30308 1.52343 1.73456 1.93773 0.82592 1.06881 1.29924 1.51899 I. 72947 1.93192 0.82331 1.06560 1.29546 1.51462 1.72447 I. 9262 0.82072 1.06243 1.29172 1.51032 1.71957 I. 9207 0.81814 1.05928 1.28803 1.50607 1.71474 1.9152 0.81557 1.05617 1.28439 1.50189 1.70999 1.9098 0.81302 1.05308 1.28078 1.49777 1.70532 1.9046 0.81048 1.05002 1.27722 1.49370 1.70073 1.8994 0.80544 1.04398 1.27021 1.48571 1.69173 1.8893 0.80045 1.03803 1.26334 1.47793 1.68300 1.8796 0.79550 1.03217 1.25661 1.47032 1.67450 1.8701 0.79059 1.02640 1.25000 1.46289 1.66621 1.8609 0.78571 1.02070 1.243.51 1.45561 1.65813 1.8520 0.78087 1.01508 1.23713 1.44848 1.65023 1.8433 0.7713 1.0040 1.2247 1.4346 1.6350 1.8266 0.7618 0.9932 1.2126 1.4213 1.6203 1.8106 0.7524 0.9827 1.2008 1.4083 1.6062 1.7953 0.7432 0.9723 1.1894 1.3958 1.5926 1.7806 0.7340 0.9621 1.1782 1.3837 1.5795 1.7665 0.6897 0.9138 1.1258 1.3274 1.5193 1.7024 0.6482 0.8692 1.0783 1.2770 1.4662 1.6465 0.6086 0.8280 1.0349 1.2312 1.4183 1.5967 0.5697 0.7896 0.9950 1.1895 1.3748 1.5517 0.5298 0.7532 0.9584 1.1513 1.3350 1.5106 0.4876 0.7181 0.9247 1.1164 1.2985 1.4728 0.4430 0.6839 0.8936 1.0845 1.2651 1.4381 0.3974 0.6507 0.8648 1.0554 1.2345 1.4061

20000 Values calculated by (15).

1.205

TABLE 5b. Water Entropy, kJ/kg-K Pbars/TOC 180 200 220 240 260 280 300 3.50 400 1 7.7482 7.8335 7.9153 7.9942 8.0702 8.1438 8.2152 8.3846 8.5432 25 2.13760 2.32926 2.51719 6.3522 6.4586 6.5543 6.6424 6.8395 7.0146 50 2.13421 2.32533 2.51258 2.69770 2.88298 6.0867 6.2067 6.4482 6.6456 100 2.12756 2.31766 2.50361 2.68702 2.86988 3.OS497 3.24697 5.9425 6.2114 150 2.1211 2.3102 2.4950 2.6768 2.8575 3.0394 3.2261 5.4404 5.8799 200 2.1147 2.3030 2.4866 2.6670 2.8458 3.0250 3.2073 3.7277 5.5521 250 2.1085 2.2959 2.4785 2.6576 2.8347 3.0114 3.1902 3.6790 5.1388 300 2.1025 2.2890 2.4707 2.6485 2.8240 2.9986 3.1744 3.6421 4.4723 350 2.0966 2.2823 2.4630 2.6398 2.8138 2.9865 3.1596 3.6118 4.2136 400 2.0907 2.2758 2.4556 2.6313 2.8040 2.9750 3.1457 3.5857 4.1134 500 2.0795 2.2631 2.4413 2.6151 2.7854 2.9534 3.1202 3.5417 4.0022 600 2.0686 2.2510 2.4278 2.5998 2.7680 2.9334 3.0970 3.5051 3.9312 700 2.0581 2.2394 2.4148 2.5853 2.7517 2.9149 3.0757 3.4733 3.8774 800 2.0479 2.2281 2.4023 2.5714 2.7362 2.8975 3.0560 3.4451 3.8335 900 2.0381 2.2173 2.3904 2.5582 2.7215 2.8811 3.0375 3.4196 3.7960 1000 2.0286 2.2068 2.3789 2.5455 2.7075 2.865.5 3.0202 3.3962 3.7632 1200 2.0103 2.1868 2.3570 2.5216 2.6812 2.8366 2.9883 3.7072

BOWERS 55

TABLE 5b. (continued)

Pbars/TOC 180 200 220 240 260 280 300 350 400 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000

1.9929 2.1680 2.3365 2.4993 1.9763 2.1501 2.3172 2.4784 1.9605 2.1331 2.2989 2.4587 1.9453 2.1168 2.2815 2.4401 1.8772 2.0445 2.0249 2.3589 1.8187 1.9832 2.1407 2.2917 I. 7670 I. 9296 2.0851 2.2340 I. 7205 1.8817 2.0358 2.1833 1.6782 I. 8384 1.9914 2.1379 I. 6395 I. 7988 1.9511 2.0967 I. 6039 I. 7625 1.9141 2.0592 1.5710 1.7289 1.8800 2.0246 1.354 1.502 1.647 1.788

2.6570 2.8101 2.9593 3.6601 2.6344 2.7856 2.9327 3.6191 2.6132 2.7628 2.9081 3.5828 2.5932 2.7414 2.8851 3.5500 2.5071 2.6501 2.7883 3.4203 2.4368 2.5766 2.7114 3.3243 2.3770 2.5145 2.6470 3.2473 2.3247 2.4607 2.5915 3.1828 2.2782 2.4130 2.5426 3.1274 2.2363 2.3702 2.4990 3.0787 2.1981 2.3314 2.4595 3.0355 2.1632 2.2960 2.4236 2.9966 1.924 2.055 2.181 2.746 1.802 1.930 2.055 2.619

Values calculated by (IS).

TABLE 5c. Water Entropy, W/kg-K Pbars/T“C 500 600 700 800 900 1000 1200 1500 2000 1 8.8342 9.0979 9.3405 9.5662 9.7781 9.9781 IO.3485 IO.8444 Il.5506 1

25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000

7.3235 7.5960 6.9760 7.2586 6.5971 6.9022 6.3452 6.6767 6.1417 6.5039 5.9616 6.3593 5.7936 6.2324 5.6320 6.1174 5.4745 6.0111 5.1780 5.8184 4.9373 5.6471 4.7669 5.4957 4.6474 5.3640 4.5590 5.2514 4.4897 5.1558 4.3849 5.0052 4.3063 4.8927 4.2430 4.8048 4.1898 4.7331 4.1437 4.6728 3.9740 4.4624 3.8570 4.3254 3.767 4.223 3.693 4.140 3.630 4.072 3.576 4.OI3 3.529 3.961 3.487 3.916 3.223 3.637

7.8436 8.0724 8.2862 8.4876 8.8597 9.3569 IO. 0640 7.5117 7.7438 7.9598 8.1626 8.5365 9.0350 9.7431 7.1671 7.4062 7.6266 7.8324 8.2100 8.7112 9.4212 6.9544 7.2009 7.4260 7.6350 8.016 8.520 9.232 6.7955 7.0498 7.2797 7.4919 7.877 9.098 6.6659 6.9282 7.1631 7.3785 7.767 8.993 6.5547 6.8254 7.0653 7.2840 7.677 8.907 6.4563 6.7355 6.9805 7.2025 7.599 8.834 6.3673 6.6551 6.9052 7.1305 7.531 8.770 6.2097 6.5148 6.7751 7.0070 7.415 8.664 6.0723 6.3942 6.6644 6.9027 7.319 8.576 5.9502 6.2878 6.5674 6.8118 7.235 8.502 5.8410 6.1926 6.4809 6.7311 7. I61 8.437 5.7431 6.1067 6.4028 6.6584 7.095 8.379 5.6552 6.0286 6.3317 6.5921 7.035 8.327 5.506 5.892 6.207 6.475 6.929 8.236 5.385 5.778 6.100 6.375 6.838 8.159 5.285 5.680 6.007 6.288 6.758 8.091 5.203 5.596 5.927 6.210 6.687 8.031 5.133 5.524 5.855 6.142 6.623 7.976 4.891 5.267 5.595 5.886 6.380 7.765 4.738 5.103 5.426 5.715 6.212 7.613 4.626 4.983 5.302 5.589 6.085 7.495 4.537 4.889 5.205 5.490 5.985 7.400 4.463 4.812 5.125 5.408 5.903 7.320 4.400 4.746 5.057 5.339 5.832 7.251 4.345 4.688 4.998 5.279 5.771 7.190 4.297 4.638 4.946 5.226 5.717 7.136 4.004 4.333 4.630 4.902 5.382 6.788 3.868 4.191 4.482 4.748 5.217 6.591 30000 3.095 3.506

56 H,O-CO2 FLUIDS

TABLE 6a. Water Heat Capacity at Constant Pressure, M/kg-K Pbars/TOC 0 20 40 60 80 100 120 140 160 1 4.228 4.183 4.182 4.183 4.194 2.042 2.005 1.986 1.977 25 SO 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000

4.215 4.202 4.177 4.153 4.130 4.109 4.089 4.070 4.053 4.021 3.992 3.967 3.945 3.926 3.909 3.880 3.856 3.833 3.810 3.786 3.61 3.32 2.89

4.175 4.168 4.153 4.139 4.125 4.112 4.100 4.087 4.076 4.054 4.034 4.015 3.998 3.983 3.968 3.942 3.919 3.899 3.880 3.861 3.76 3.60 3.32 2.85

4.176 4.170 4.159 4.148 4.137 4.126 4.116 4.106 4.097 4.078 4.061 4.045 4.030 4.015 4.002 3.977 3.955 3.936 3.918 3.901 3.83 3.77 3.71 3.68 3.67 3.64

4.177 4.189 4.211 4.243 4.282 4.172 4.183 4.206 4.237 4.275 4.161 4.173 4.195 4.224 4.261 4.151 4.163 4.184 4.212 4.247 4.141 4.153 4.174 4.201 4.234 4.131 4.143 4.163 4.190 4.222 4.122 4.133 4.154 4.179 4.210 4.113 4.124 4.144 4.169 4.198 4.104 4.115 4.135 4.159 4.187 4.086 4.098 4.117 4.140 4.165 4.070 4.082 4.100 4.121 4.145 4.054 4.066 4.083 4.104 4.126 4.040 4.051 4.068 4.087 4.108 4.026 4.037 4.053 4.072 4.091 4.012 4.023 4.039 4.057 4.075 3.988 3.998 4.013 4.030 4.045 3.965 3.975 3.989 4.004 4.019 3.945 3.954 3.967 3.981 3.994 3.926 3.935 3.947 3.961 3.972 3.909 3.917 3.929 3.941 3.951 3.84 3.85 3.85 3.86 3.87 3.79 3.79 3.80 3.81 3.82 3.77 3.76 3.76 3.77 3.77 3.80 3.74 3.72 3.73 3.74 3.89 3.77 3.70 3.70 3.71 4.06 3.83 3.69 3.66 3.68 4.29 3.95 3.70 3.64 3.65 4.53 4.09 3.72 3.61 3.62

4.332 4.323 4.306 4.290 4.275 4.260 4.246 4.233 4.220 4.195 4.172 4.151 4.131 4.112 4.094 4.061 4.032 4.005 3.981 3.959 3.87 3.82 3.77 3.74 3.72 3.69 3.67 3.64 3.22

TABLE 6b. Water Heat Capacity at Constant Pressure, kJkg-K Pbars/TOC 180 200 220 240 260 280 300 350 400 1 1.974 I.975 1.980 1.986 1.994 2.003 2.013 2.040 2.070 25 4.397 4.484 4.602 2.903 2.678 2.532 2.433 2.299 2.245 50 4.386 4.469 4.583 4.740 4.967 3.614 3.181 2.672 2.468 100 4.365 4.442 4.547 4.689 4.889 5.186 5.675 4.027 3.100 150 4.345 4.417 4.513 4.643 4.821 5.076 5.470 8.838 4.177 200 4.327 4.394 4.482 4.601 4.761 4.983 5.311 8.138 6.371 250 4.309 4.372 4.454 4.562 4.707 4.904 5.182 6.994 13.270 300 4.292 4.350 4.427 4.527 4.659 4.834 5.075 6.401 25.080 350 4.276 4.331 4.402 4.494 4.615 4.773 4.984 6.022 11.671 400 4.260 4.312 4.378 4.464 4.575 4.718 4.906 5.752 8.717 500 4.231 4.277 4.335 4.409 4.504 4.623 4.775 5.384 6.789 600 4.204 4.245 4.296 4.361 4.443 4.544 4.670 5.138 6.011 700 4. I80 4.216 4.261 4.318 4.390 4.477 4.584 4.959 5.571 800 4.157 4.189 4.229 4.280 4.342 4.419 4.510 4.820 5.280 900 4.135 4.164 4.200 4.245 4.300 4.367 4.447 4.708 5.071 1000 4.115 4.141 4.173 4.213 4.262 4.321 4.391 4.615 4.911 1200 4.078 4.099 4.124 4.156 4.196 4.243 4.298 4.469 4.678

BOWERS 57

TABLE 6b. (continued)

Pbars/TOC 180 200 220 240 260 280 300 350 400

1400 4.046 4.062 4.082 4.108 4.140 4.178 4.223 4.357 4.515

1600 4.016 4.03 4.05 4.07 4.09 4.12 4.16 4.27 4.39

1800 3.990 4.00 4.01 4.03 4.05 4.08 4.11 4.20 4.30

2000 3.966 3.97 3.98 4.00 4.01 4.03 4.06 4.13 4.22

3000 3.87 3.87 3.87 3.88 3.88 3.89 3.90 3.93 3.97

4000 3.81 3.81 3.80 3.80 3.79 3.79 3.80 3.81 3.83

5000 3.77 3.76 3.75 3.74 3.74 3.73 3.73 3.73 3.74

6000 3.74 3.73 3.72 3.70 3.69 3.69 3.68 3.68 3.68

7000 3.71 3.70 3.69 3.68 3.67 3.65 3.65 3.63 3.63

8000 3.69 3.68 3.67 3.66 3.64 3.63 3.62 3.60 3.60

9000 3.67 3.67 3.66 3.64 3.63 3.61 3.60 3.58 3.57

10000 3.66 3.66 3.64 3.63 3.61 3.60 3.59 3.56 3.55

20000 3.37 3.47 3.53 3.56 3.56 3.56 3.55 3.51 3.47

30000 3.46 3.50 3.52 3.51 3.48 Values calulated by (15).

TABLE 6c. Water Heat Capacity at Constant Pressure, kJ/kg-K Pbars/TOC 500 600 700 800 900 1000 1200 1500 2000

1 2.135 2.203 2.273 2.343 2.412 2.478 2.599 2.750 2.931 25 2.228 50 2.335 100 2.584 150 2.891 200 3.269 250 3.737 300 4.312 350 5.006 400 5.799 500 7.239 600 7.534 700 6.992 800 6.383 900 5.908 1000 5.557 1200 5.092 1400 4.801 1600 4.60 1800 4.46 2000 4.34 3000 4.02 4000 3.86 5000 3.75 6000 3.68 7000 3.63 8000 3.59 9000 3.56 10000 3.53 20000 3.42

2.259 2.310 2.370 2.431 2.493 2.608 2.755 2.934 2.322 2.351 2.398 2.452 2.508 2.618 2.761 2.937

2.458 2.437 2.456 2.494 2.540 2.64 2.77 2.94 2.610 2.529 2.518 2.538 2.573 2.66 2.78 2.95 2.778 2.627 2.583 2.583 2.606 2.68 2.79 2.95

2.961 2.729 2.649 2.630 2.640 2.70 2.80 2.96 3.160 2.836 2.716 2.677 2.674 2.72 2.81 2.96 3.373 2.945 2.785 2.724 2.709 2.74 2.83 2.97

3.597 3.057 2.854 2.771 2.743 2.76 2.84 2.97 4.062 3.283 2.992 2.866 2.812 2.80 2.86 2.98 4.500 3.503 3.126 2.957 2.879 2.84 2.88 2.99 4.846 3.705 3.253 3.045 2.943 2.88 2.90 3.00 5.058 3.880 3.369 3.126 3.004 2.91 2.92 3.01

5.138 4.022 3.472 3.201 3.061 2.95 2.94 3.02 5.123 4.129 3.561 3.269 3.113 2.98 2.96 3.03

4.955 4.246 3.698 3.382 3.204 3.04 3.00 3.05 4.754 4.270 3.785 3.468 3.277 3.10 3.03 3.06 4.58 4.24 3.83 3.53 3.34 3.14 3.06 3.08 4.44 4.19 3.85 3.57 3.38 3.18 3.08 3.09 4.33 4.13 3.85 3.60 3.41 3.21 3.11 3.11 4.00 3.90 3.76 3.61 3.48 3.30 3.18 3.16 3.84 3.77 3.68 3.58 3.48 3.34 3.23 3.19 3.74 3.69 3.62 3.54 3.47 3.35 3.25 3.21

3.67 3.63 3.58 3.51 3.45 3.35 3.26 3.22 3.62 3.5.9 3.54 3.49 3.44 3.35 3.27 3.23 3.58 3.55 3.52 3.47 3.42 3.34 3.27 3.23 3.55 3.53 3.49 3.45 3.41 3.34 3.27 3.24 3.52 3.50 3.47 3.44 3.40 3.34 3.27 3.24 3.39 3.37 3.35 3.33 3.31 3.28 3.24 3.22 3.35 3.32 3.29 3.26 3.23 3.20 3.17 3.16 30000 3.41


58 H20-CO2 FLUIDS

TABLE 7. Water Properties at Saturation T,“C P,bars “hq “gas “bq H gas ‘liq S 0.01 0.0061173 18.0200 3711116. 0.00 2500.5 0. ooooo P.la;41 IO 0.012281 18.0216 20 0.023388 18.0488 30 0.042455 18.0955 40 0.073814 18.1581 50 0.12344 18.2349 60 0.19932 18.3244 70 0.31176 18.4260 80 0.47373 18.5388 90 0.70117 18.6630 100 I.0132 18.7981 120 1.9848 19.1018 140 3.6119 19.4519 160 6.1766 19.8524 180 10.019 20.3098 200 15.537 20.8339 220 23. I78 21.4390 240 33.447 22.1456 260 46.895 22.9846 280 64.132 24.0049 300 85.838 25.2889 320 112.79 26.995 7 340 145.94 29,4976 360 186.55 34.1151 365 198.09 36.2482 370 210.30 39.7577 373.5 219.30 46.7948 373.976 220.55 55.958

1915461. 1040928. 592654. 351816. 216859. 13825.5. 90884. 61413. 42548. 30152. 16074. 9170.0 5532.5 3495.6 2293.8 1552.3 1076.3 760.17 543.43 390.35 278.82 194.36 125.43 108.60 89.954 69.560

41.99 83.84 125.67 167.50 209.33 251. I5 293.01 334.93 376.93 419.06 503.78 589.24 675.65 763.25 852.38 943.51 1037.24 1134.38 1236.08 1344.05 1461.25 1593.8 1761.0 1816.7 1889.7 1991.6 2086

2518.9 2537.2 2555.3 2573.4 2591.2 2608.8 2626.1 2643.1 2659.6 2675.7 2706.2 2733.8 2758.0 2777.8 2792.5 2801.3 2803.0 2796.2 2779.2 2748.7 2699.7 2621.3 2482.0 2424.6 2340.2 2207.3

0.15097 0.29621 0.43653 0.57228 0.703 74 0.83119 0.95494 1.07530 1.19253 1.30689 1.52776 1.73936 1.94293 2.13966 2.33076 2.51753 2.70135 2.88382 3.06691 3.25336 3.44760 3.6587 3.9153 3.9994 4.1094 4.2640 4.409

8.8986 8.6651 8.4513 8.2550 8.0745 7.9080 7.7540 7.6112 7.4784 7.3545 7.1297 6.9302 6.7503 6.5853 6.4312 6.2847 6.1423 6.0009 5.8565 5.7042 5.5356 5.3345 5.0542 4.9520 4.8098 4.5977


TABLE Sa. Water Sound Speed, m/set PbarslTOC 0 20 40 60 80 100 120 140 160 1 1401.0 1483.2 1528.4 1549.5 1552.8 472.8 486. I 498.7 510.8 25 1405.2 1487.5 1532.9 1554.3 1558. 1547.3 1524.3 1490.5 1447.0 50 1409.6 1491.9 1537.5 1559.2 1563.3 1553.0 1530.6 1497.4 1454.6 100 1418.1 1500.6 1546.6 1568.9 1573.7 1564.3 1542.8 1510.8 1469.4 150 1426.5 1509.2 1555.6 1578.5 1584.0 1575.4 1554.8 1523.9 1483.8 200 1434.9 1517.6 1564.4 1587.9 1594.0 1586.2 1566.5 1536.6 1497.7 250 1443. I 1526.0 1573.1 1597. I 1603.9 1596.8 1577.9 1549.0 1511.3 300 1451.3 1534.2 1581.7 1606.2 1613.5 1607.1 1589.1 1561.1 1524.5 350 1459.6 1542.4 1590.2 1615.1 1623.1 1617.3 1600.1 1573.0 1537.4 400 1467.9 1550.6 1598.6 1623.9 1632.4 1627.3 1610.8 1584.6 I550.0 500 1484.6 1566.8 1615.1 1641.2 1650.7 1646.8 1631.7 1607.0 1574.2 600 1501.9 1583.0 1631.4 1658.1 1668.5 1665.7 1651.8 1628.6 1597.4 700 1519.6 1599.2 1647.5 1674.6 1685.9 1684.0 1671.3 1649.4 1619.7 800 1538.1 1615.5 1663.4 1690.9 1702.8 1701.9 1690.2 1669.5 1641.1 900 1557.3 1632.0 1679.2 1706.9 1719.4 1719.2 1708.5 1688.9 1661.8 1000 1577.1 1648.6 1695.0 1722.7 1735.6 1736.2 1726.3 1707.7 1681.8 1200 1619.0 1682.6 1726.5 1753.8 1767.3 1769.0 1760.7 1743.8 1719.9 1400 1663.1 1717.3 1757.9 1784.4 1798.1 1800.6 1793.4 I 778.0 1755.8 1600 1708.9 1752.7 1789.4 1814.6 1828.1 1831.1 1824.9 1810.7 1789.9

BOWERS 59

TABLE 8a. (continued) Pbars/TOC 0 20 40 60 80 100 120 140 160

1800 1755.5 2000 1802.0 3000 2012. 4000 2161. 5000 2273. 6000 7000 8000 9000 10000 20000 30000


1788.4 1821.0 1844.4 1857.5 1860.8 1855.2 1842.0 1822.3 1824.3 1852.5 1874.0 1886.3 1889.6 1884.5 1872.1 1853.4 1990. 2005. 2018. 202.5. 2025. 2020. 2009. 1993. 2108. 2135. 2152. 2154. 2149. 2141. 2129. 2113. 2163. 2234. 2272. 2275. 2265. 2252. 2237. 2221. 2181. 2316. 2382. 2388. 2374. 2356. 2337. 2318.

2423. 2493. 2497. 2476. 2453. 2430. 2408. 2606. 2619. 2603. 2574. 2544. 2517. 2492.

2766. 2711. 2667. 2630. 2598. 2571. 2928. 2821. 2758. 2711. 2675. 2644.

3227.

TABLE 8b. Water Sound Speed, m/see PbarslT’C 180 200 220 240 260 280 300 350 400 1 522.4 533.7 544.7 555.3 565.7 575.8 585.7 609.5 632.2 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000

1394.4 1333.0 1262.4 521.7 1402.9 1342.6 1273.5 1194.6 1419.4 1361.3 1294.9 1219.7 1435.4 1379.2 1315.3 1243.3 1450.8 1396.4 1334.8 1265.7 1465.8 1413.0 1353.4 1287.0 1480.3 1429.1 1371.4 1307.3 1494.4 1444.6 1388.7 1326.7 1508. I 1459.7 1405.4 1345.4 1534.4 1488.5 1437.1 1380.6 1559.5 1515.8 1466.9 1413.4 1583.5 1541.7 1495.0 1441.1 1606.5 1566.4 1521.7 1473.0 1628.5 1590.0 1547.1 15oo.s 1649.8 1612.7 1571.4 1526.5 1690.1 1655.5 1617.0 1575.2 1727.9 1695.4 1659.2 1619.9 1763.6 1733. 1699. 1662. 1797.4 1768. 1736. 1700. 1829.7 1802. 1771. 1737. 1973. 1949. 1923. 1894. 2094. 2072. 2048. 2022. 2201. 2180. 2157. 2132. 2298. 2276. 2253. 2229. 2386. 2364. 2341. 2316. 2468. 2445. 2420. 2396. 2545. 2520. 249.5. 2470. 2616. 2590. 2564. 2538. 3177. 3135. 3099. 3065.

537.6 551.9 565.1 594.8 621.3 1104.1 519.0 538.4 577.3 608.9 1134.3 1036. I 919.7 533.2 581.0 1162.4 1070.6 964.6 464.1 547.5 1188.6 1102.3 1004.4 662.0 505.8 1213.3 1131.6 1040.2 744.7 448.6 1236.6 1158.9 1073.0 808.3 419.0 1258.8 1184.4 1103.2 861.1 536.1 1279.8 1208.6 1131.3 906.8 627.3 1319.2 1253.2 1182.4 983.8 756.3 1355.6 1293.7 122s. 1 1048.0 850.7 1389.3 1331.0 1269.6 1103.6 926.6 1420.9 1365.6 1307.6 1152.9 990.8 1450.6 1397.9 1342.9 1197.4 1046.8 1478.7 1428.3 1375.8 1238.0 1096.7 1530.8 1484.2 1435.9 1310.2 1183.1 1578.3 1534.8 1489.7 1373.4 1256.6 1622. 1581. 1539. 1430. 1321. 1663. 1624. 1584. 1481. 1379. 1701. 1664. 1626. 1528. 1431. 1864. 1832. 1800. 1718. 1638. 1995. 1967. 1938. 1865. 1793. 2106. 2080. 2053. 1985. 1918. 2204. 2179. 2153. 2087. 2023. 2292. 2267. 2241. 2178. 2116. 2371. 2346. 2321. 2259. 2198. 2445. 2420. 2395. 2333. 2273. 2.513. 2488. 2462. 2401. 2342. 3034. 3004. 2976. 2910. 2850. 3423. 3389. 335 7. 3285. 3221.


60 H20-CO2 FLUIDS

TABLE 8c. Water Sound Speed, m/set PbarsfT’C 500 600 700 800 900 IO00 1200 1500 2000

674.6 713.9 750.7 785.3 818.3 849.8 909.3 991.7 1115.9 1 25 50 100 150 200 250 300 350 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000

7000 8000 9000

10000 20000 30000

668.3 710.2 748.6 784.3 817.9 850.0 910. I 993. I 1117.7 661.6 706.4 746.5 783.3 817.7 850.3 911.1 994.6 1119.5 647.7 698.9 742.6 781.7 817.6 851.2 913. 998. 1123. 633.3 691.7 739.1 780.4 817.8 852.5 916. 1001. 1127. 618.9 684.8 736.0 779.5 818.3 853.9 918. 1005. 1131. 604.5 678.4 733.2 778.8 819.0 855.5 921. 1008. 1135. 590.9 672.7 730.8 778.4 819.9 857.2 924. 1012. 1139. 579.0 667.8 729.0 778.3 820.9 859.0 927. 1015. 1143. 570.4 664.1 727.7 778.5 822.1 861.0 930. 1019. 1146. 572.2 661.2 727.3 780.1 825.2 865.2 935. 1026. 1154. 608.0 666.1 730.3 783.6 829.4 870.1 941. 1033. 1162. 667.0 680.2 737.5 789.3 834.9 875.8 948. 1039. 1169. 732.6 702.9 748.9 797.4 841.8 882.4 954. 1047. 1176. 796.3 732.6 764.2 807.9 850.4 890.0 961. 1054. 1184. 855.6 767.3 783. I 820.8 860.5 898.8 969. 1061. 1191. 960.2 843.8 829.0 852.3 885.1 919.4 986. 1076. 1205. 1049.1 921.2 882.1 890.0 914.4 943.8 1005. 1092. 1220. 1126. 99s. 938. 932. 947. 971. 1026. 1109. 123.5. 1194. 1062. 995. 976. 982. 1001. 1049. 1127. 1250. 1255. 1125. 10.50. 1021. 1019. 1032. 1073. 1146. 1265. 1491. 1373. 1288. 1234. 1205. 1194. 1202. 1247. 1344. 1660. 1552. 1469. 1409. 1370. 1346. 1331. 1352. 1426. 1795. 1692. 1611. 15.51. 1508. 1478. 1449. 1452. 1507. 1906. 1808. 1729. 1669. 1624. 1591. 1554. 1544. 1584. 2002. 1906. 1829. 1769. 1723. 1689. 1648. 1629. 1657. 2087. 1993. 1916. 1856. 1809. 1774. I730. 1706. 1725. 2163. 2070. 1994. 1933. 1886. 1850. 1804. 1776. 1788.

2233. 2140. 2064. 2003. 1955. 1918. 1870. 1839. 1847. 2740. 2643. 2560. 2490. 2430. 2381. 2310. 2254. 2242.

3107. 3006. 2916. 2836. 276.5. 2704. 2605. 2511. 2459. Values calculated by (15).

Pbars/T’C 0 1 87.90 10 87.94 50 88.10 100 88.29 200 88.75 300 89.20 400 89.64 500 90.07 600 PO. 48 700 90.88 800 91.27 900 91.65 1000 92.02 1200 92.73 1400 93.39 1600 94.01

TABLE 9a. Water Dielectric Constant 25 50 75 100 125 150 175 78.38 69.88 62.28 55.51 1.01 1.00 1.00 78.41 69.91 62.32 55.55 49.50 44.08 39.20 78.56 70.05 62.46 55.69 49.65 44.24 39.36 78.85 70.27 62.60 55.78 49.71 44.31 39.47 79.24 70.63 62.94 56.11 50.06 44.67 39.85 79.62 70.98 63.28 56.44 50.39 45.01 40.21 79.99 71.32 63.60 56.76 50.71 45.33 40.55 80.36 71.65 63.92 57.07 51.02 45.65 40.88 80.72 71.98 64.23 57.38 51.32 45.96 41.19 81.07 72.30 64.53 57.67 51.61 46.25 41.50 81.41 72.61 64.83 57.96 51.90 46.54 41.79 81.74 72.92 65.12 58.24 52.18 46.82 42.08

82.07 73.22 65.41 58.52 52.45 47.10 42.36

82.70 73.81 65.96 59.06 52.98 47.62 42.89 83.30 74.37 66.49 59.57 53.49 48.13 43.40 83.88 74.91 67.01 60.07 53.97 48.61 43.88

BOWERS 61

Pbars/T’C 0 25

1800 94.59 84.43 2000 95.14 84.96 2500 96.37 86.19 3000 97.44 87.30 3500 98.40 88.31 4000 99.25 89.26 4500 100.04 90.14 5000 100.77 90.99 6000 92.60 7000 8000 9000 10000

Values calculated by (15) and (2).

TABLE 9a. (continued) 50 75 100 125 150 175

75.43 67.50 60.55 54.44 49.07 44.34 75.93 67.98 61.01 54.89 49.52 44.79 77.11 69.11 62.10 55.95 50.56 45.82 78.19 70. I6 63.11 56.94 51.53 46.78 79.18 71.13 64.05 57.86 52.42 47.66 80. I1 72.03 64.93 58.71 53.26 48.48 80.98 72.87 65.76 59.52 54.05 49.26 81.79 73.66 66.53 60.28 54.80 49.98 83.30 75.11 67.96 61.68 56.17 51.33 84.69 76.41 69.24 62.95 57.42 52.55 85.95 77.58 70.40 64.10 58.55 53.66

78.65 71.45 65.16 59.60 54.69 79.62 72.41 66.13 60.57 55.64

TABLE 9b. Water Dielectric Constant Pbars/T’C 200 225 250 275 300 325 350 375 1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 10 50 100 200 300 400 500 600 700 800 900 1000 1200 1400 1600 1800 2000 2500 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000

1.04 34.93 35.11 35.51 35.90 36.26 36.61 36.94 37.26 37.57 37.86 38.15 38.70 39.21 39.70 40.17 40.61 41.65 42.59 43.47 44.28 45.04 45.75 47.07 48.26 49.3.5 50.36 51.29

1.03 30.86 31.12 31.57 31.99 32.39 32.76 33.12 33.46 33.78 34.09 34.39 34.96 35.49 35.99 36.46 36.91 37.95 38.90 39.76 40.57 41.32 42.02 43.31 44.47 45.54 46.52 47.43

Values calculated by (15) and (2).

1.03 27.05 27.42 27.94 28.42 28.86 29.27 29.66 30.02 30.37 30.70 31.01 31.61 32.16 32.67 33. I6 33.61 34.67 35.62 36.48 37.28 38.02 38.71 39.98 41.12 42.16 43.11 43.99

1.03 1.19 23.90 24.54 25.10 25.60 26.07 26.49 26.89 27.27 27.62 27.96 28.58 29.16 29.69 30.19 30.66 31.73 32.69 33.55 34.35 35.08 35.76 37.01 38.13 39.14 40.07 40.92

1.03 1.02 1.02 1.02 1.16 1.14 1.13 1.12 20.40 1.28 1.23 1.20 21.25 17.91 14.09 2.00 21.95 18.86 15.69 12.03 22.55 19.63 16.75 13.78 23.09 20.27 17.57 14.90 23.57 20.84 18.25 15.75 24.02 21.35 18.84 16.46 24.43 21.81 19.37 17.07 24.82 22.23 19.84 17.61 25.18 22.63 20.28 18.10 25.85 23.35 21.06 18.94 26.45 23.99 21.74 19.68 27.01 24.57 22.36 20.33 27.53 25.11 22.92 20.92 28.01 25.61 23.44 21.45 29. IO 26.73 24.58 22.63 30.07 27.71 25.57 23.63 30.93 28.58 26.45 24.51 31.72 29.37 27.23 25.30 32.45 30.09 27.95 26.01 33.13 30.76 28.61 26.67 34.36 31.96 29.80 27.83 35.45 33.03 30.84 28.85 36.43 33.99 31.78 29.75 37.33 34.86 32.62 30.56 38.16 35.66 33.39 31.30

62 H,O-CO, FLUIDS

TABLE 9c. Water Dielectric Constant Pbars/T"C 400 450 500 600 700 800 900 1000 1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 10 50 100 200 300 400 500 600 700 800 900 1000 1200 1400 1500 1600 1800 2000 2500 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000

1.00 1.02 1.11 1.17 1.64 5.95 10.47 12.18 13.31 14.18 14.90 15.52 16.06 17.00 17.79

1.02 1.01 1.01 1.09 1.08 1.06 1.14 1.11 1.08 1.42 I.32 1.22 2.07 1.68 I.41 3.85 2.34 I.69 6.58 3.44 2.07 8.54 4.89 2.57 9.89 6.31 3.17 10.90 7.50 3.83 11.72 8.48 4.52 12.40 9.29 5.21 13.53 10.60 6.46 14.44 11.63 7.53

1.01 1.01 1.01 1.01 1.05 1.04 1.03 1.03 1.10 I.08 1.07 1.06 I.23 I.18 1.15 1.13 1.38 I.29 1.24 1.20 1.56 1.43 1.34 1.28 1.78 1.57 1.45 1.36 2.04 1.74 1.57 1.46 2.32 1.92 1.70 1.56 2.64 2.12 1.84 1.66

3.34 2.56 2.15 1.89

15.21 15.88 16.48 17.74 18.78 19.67 20.44 21.13 21.75 22.84 23.76 24.56 25.26

29.36 25.87 Values calculated by (15) and (2).

18.47 19.09 19.65 20.85 21.87 22.75 23.54 24.24 24.89 26.03 27.02 27.89 28.66

12.48 13.20 13.83 15.14 16.19 17.07 17.83 18.49 19.08 20.09 20.93 21.64 22.25 22.77

8.42 9.19 9.85 11.18 12.20 13.03 13.71 14.29 14.79 15.59 16.21 16.69 17.05 17.32

5.09 3.76 3.00 2.53

6.57 4.89 3.85 3.18 7. 75 5.89 4.65 3.81 8.73 6.75 5.37 4.41 9.55 7.49 6.02 4.96 10.27 8.15 6.60 5.47 10.90 8.73 7.13 5.94 11.48 9.26 7.61 6.37

3. CARBON DIOXIDE

3.1 Volume Volumes of carbon dioxide are compiled from 0” to

1000°C and 25 bars to 40 Kbar. Values given in Table lOa-b to a maximum pressure of 10 Kbar are taken from experimental studies by (21), (20), (39) and (35). Values from 20 to 40 Kbar are derived from the EOS given by (29). Table 11 gives shock-compressed data at higher pressures and temperatures, calculated by (31). Additional shock experiment data can be found in (32).

3.2 Dielectric Constant Dielectric constants of carbon dioxide have not been mea-

sured. They are of interest because they must be known in order to predict the effect that adding carbon dioxide to water will have on the dielectric constant of the fluid.

Therefore, dielectric constants of carbon dioxide are presented here, where they are calculated after the method given in (40) by:

(2e+l)(c-1) 4xwpa 9~2 = 3M

where e is the dielectric constant, N” is Avogadro’s number, p is the density, M is the molecular weight, and CY is the molecular polarizability of carbon dioxide. A value of 2.63 x 1O-24 cm’ is used for the molecular polarizability . Dielectric constants are calculated from 0” to 1000°C and 50 bars to 10 Kbars, at the same pressure-temperature points for which volume or density information for carbon dioxide is available. These calculated values are given in Table 12a-b.

BOWERS 63

TABLE 10a. Carbon Dioxide Volume, cm3/mole Pbars/T’C 0 20 40 60 80 100 150 200 250 300

?< 732.3 835.1 924.6 1007. 1084. 1164. 1354. 1528. 1712. 1889. ;; 75 100 150 200 2.50 300 350 400 450

500 600 700 800 900 1000 1200 1400

1500 2000 2500

3000 3500 4000

5000 6000 7000 8000 9000 10000 20000 30000 40000

46.5 309.3 387.8 447.3 498.4 46.1 54.3 190.9 255.0 299.6 45.4 51.5 69.0 153.5 198.7 44.1 48.8 56.1 72.9 102.4 43.28 47.15 52.30 60.79 74.16 42.52 45.84 50.18 55.79 64.04 41.80 44.76 48.49 53.08 58.95 41.25 43.88 47.13 50.97 55.72 40.78 43.15 46.04 49.42 53.39 40.38 42.52 45.12 48.16 51.68 39.92 41.99 44.38 47.12 50.22 39.20 41.06 43.13 45.44 48.01 38.59 40.27 42.12 44.13 46.34 38.04 39.61 41.29 43.11 45.05 37.62 39.04 40.57 42.21 43.97 37.17 38.50 39.93 41.45 43.07 36.37 37.56 38.83 40.16 41.56 35.77 36.83 37.96 39.14 40.38

543.3 337.2 234.5 132.2 91.40 74.85 66.38 61.47 58.13 55.63 53.70

50.85 48.70 47.14

45.84 44.77 43.02 41.66 41.08 38.70 37.16

35.92 35.02

34.20 33.04 31.97 31.02 30.21 29.57 29.01 25.84 24.70 24.07

653.0 417.6 301.2 188.3 134.7 106.0 89.36 79.31 72.40 67.70

63.89 58.92 55.51 52.97

51.01 49.38 46.89 45.00 44.14

41.18 39.07

751.0

490.1 360.7 23 1.6 169.9 134.5 112.6 98.00 87.92 80.86 75.45

67.87 62.89 59.29

56.50 54.26 50.97 48.51 47.37 43.73 41.24

39.34 38.06

36.90 35.11 33.64 32.38 31.48 30.62 29.87 26.72 25.35 24.60

849.6 558.5 413.2 270.2 200.8 160.4 134.4 116.6 103.9 94.20

86.91 77.09 70.49 65.82

62.29 59.39 55.21 52.14 50.72 46.33 43.42

41.23 39.48

910.4

622.5 462.8 306.9 218.9 181.3 154.4 131.2 119.2 108.1 99.03

86.50 78.23 72.13 68.16 61.67 59.55 55.78 51.16

48.93 45.56 43.11

41.20 39.57 37.17

35.29 33.73 32.74 31.67 30.72 27.51 25.95 25.08

Values from (21), (20), (39), (35) and (29).

TABLE lob. Carbon Dioxide Volume, cm3/mole Pbars/T“C 350 400 450 500 600 700 800 900 1000 25 2066. 2234. 2405. 2574. 2915. 3260. 3607. 3930. 4273. 50 1031. 1120. 1206. 1294. 1462. 1636. 1804. 1974. 2147. 75 684.5 744.7 804.6 864.7 980.2 1095. 1209. 1322. 1434. 100 513.5 558.5 606.2 650.1 737.2 824.2 909.3 995.7 1081. 150 340.6 373.6 405.3 436.2 496.2 554.3 613.0 669.9 728.7 200 255.1 281.2 305.4 328.7 374.9 420.0 464.3 507.0 552.2 250 205.9 226.6 246.4 265.4 303.5 339.6 375.2 410.2 446.4 300 173.3 190.7 207.9 224.3 255.6 286.2 316.4 346.0 374.9 350 150.3 166.1 181.0 195.3 222.4 249.1 274.6 299.8 326.0 400 134.0 147.7 160.7 173.5 197.6 220.9 243.7 265.6 288.2 450 121.0 133.7 145.8 157.1 179.1 199.6 219.1 239.1 259.3 500 110.9 122.2 132.9 143.5 163.4 181.9 200.3 217.9 235.6 600 96.03 105.5 114.6 123.5 140.2 156.1 171.4 186.1 200.6

64 H20-CO* FLUIDS

TABLE lob. (continued)

Pbars/T’C 3.50 400 450 500 600 700 800 900 1000

700 800 900 1000 1200 1400 1500 2000 2500

3000 3500 4000

5000 6000 7000 8000 9000 10000 20000 30000

40000

86.01 93.96 79.11 85.79 74.03 79.82 69.96 75.12 63.93 68.23 59.47 63.15 57.60 51.47 53.90 47.65 49.60

44.97 46.76 42.86 44.43 41.11 42.25

39.24 36.96 35.09 34.01 32.72 31.58 28.24 26.50

25.54

101.8 109.5 123.9 137.5 150.9 163.7 175.8

92.50 99.17 111.9 123.9 135.5 146.8 157.4

85.51 91.23 102.6 113.5 123.6 133.5 142.9

80.21 85.21 95.26 105.0 114.1 123.0 131.5

72.37 76.45 84.51 92.27 99.96 107.3 114.3 66.77 70.26 77.01 83.64 90.04 96.24 102.2

Values from (21), (20), (39), (35) and (29).

56.14 59.19 51.39

48.45 50.03 45.87

45.10 41.71 39.13 37.03 35.28 33.76 32.43 28.93 27.02 25.97

64.26 69.33 74.41 79.48 84.55

53.51 56.99 60.47 63.96 67.44

47.82 50.53 53.25 55.97 58.69

43.92 46.13 48.34 50.54 52.75 40.95 42.78 44.61 46.43 48.26

38.56 40.08 41.60 43.12 44.64 36.54 37.81 39.08 40.34 41.61 34.81 35.86 36.91 37.95 39.00 33.29 34. IS 35.00 35.86 36.71

29.58 30.20 30.80 31.38 31.94 27.52 27.99 28.45 28.89 29.32

26.37 26.77 27.14 27.51 27.86

TABLE 11. Shock-Compressed Carbon Dioxide Data Pressure Volume Temperature Wb) (cm3/m) 0-Q

275.2 * 2.4 17.36 &- 0.18 3800 340. 17. 4500 421.9 f 3.2 15.96 + 0.16 5500 545.3 + 5.3 14.17 + 0.23 6600 708.2 f 7.4 13.16 + 0.25 8100

Values from (31).

TABLE 12a. Carbon Dioxide Dielectric Constant Pbars/T“C 0 20 40 60 80 100 150 200 250 300

50 1.480 1.066 1.052 1.045 1.041 1.037 1.031 1.027 1.024 1.021 100 1.492 I.430 1.314 1.135 1. I03 1.087 1.067 1.056 I.049 1.044 150 1.508 1.455 1.392 1.296 1.206 1.158 1.109 1.088 1.076 1.066 200 1.519 1.473 1.422 1.359 1.291 1.233 I.155 1.122 1.102 1.089 300 1.539 1.500 1.459 1.416 1.371 1.327 1.238 1.187 l.lS.5 1.134 400 1.554 1.521 1.485 1.449 1.413 1.377 1.298 1.242 1.203 1.176 500 1.567 1.537 1.505 1.473 1.442 1.411 1.340 1.285 1.245 1.213 600 1.578 1.550 1.521 1.492 1.464 1.435 1.371 1.319 1.279 1.247 700 1.589 1.562 1.535 1.508 1.482 1.457 1.396 I.346 1.307 1.274 800 1.598 1.572 1.547 1.521 1.497 1.473 1.417 1.369 1.330 1.297 900 I.605 1.581 I.557 1.533 1.510 1.488 1.434 1.389 1.349 I.317 1000 1.613 1.590 1.567 1.544 1.522 1.500 1.449 1.406 1.368 1.336

BOWERS 65

TABLE 12a. (continued) Pbars/TOC 0 20 40 60 80 100 150 200 250 300

1200 1.628 1.606 1.584 1.563 1.542 1.523 1.475 1.434 1.398 1.367 1400 1.640 1.620 1.599 1.579 1.560 1.541 1.497 1.458 1.423 1.394 1500 I.549 1.508 1.471 1.436 1.407 2000 1.583 1.548 1.510 1.482 1.453 3000 1.633 1.573 1.547 1.522 4000 1.672 1.618 1,571 5000 1.702 1.653 1.611 6000 1.728 1.684 1.645 7000 1.751 1.711 1.677 8000 1.771 1.737 1.705 9000 1.789 1.759 1.732 10000 1.806 1.781 1.757

Values calculated after method of (40).

TABLE 12b. Carbon Dioxide Dielectric Constant Pbars/T”C 350 400 450 500 600 700 800 900 1000 50 1.019 1.018 1.017 1.015 1.014 1.012 1.011 1.010 1.010 100 1.039 150 1.059 200 1.080 300 1.119 400 1.155 500 1.190 600 1.221 700 1.248 800 1.271 900 1.291 1000 1.309 1200 1.340 1400 1.368 1500 I.381 2000 1.430 3000 1.498 4000 1.549 5000 6000 7000 8000 9000 10000

1.036 1.054 1.072 1.108 1.140 1.171 1.200 I.226 1.249 1.268 1.286 1.317 1.345

1.407 1.479 1.531 I..574 I.611 1.644 1.677 1.705 I. 734

1.033 1.031 1.050 1.046 1.066 1.062 1.099 1.091 1.129 1.119 1.157 1.145 1.183 1.169 1.207 I.192 1.229 1.213 1.249 1.233 1.267 1.250 1.298 1.281 1.325 1.308

1.391 1.370 1.459 1.443

1.496 1.540 1.580 1.616 1.649 1.682 1.712

1.027 1.025 1.022 1.020 1.019 1.041 1.036 1.033 1.030 1.028 1.054 1.048 1.043 1.040 1.036 1.080 1.071 1.064 1.059 1.054 1.104 1.093 1.084 1.077 1.071 1.126 1.114 1.103 1.094 1.087 1.148 1.133 1.121 1.110 1.102 1. I69 I. 151 1.137 I. 126 I.117 1.188 1.169 1.154 1.141 1.132 1.206 1.185 1.169 1.156 1.145 1.222 1.201 1.184 1.170 1.159 1.252 1.230 1.211 1.196 1.184 1.279 1.255 1.236 1.220 1.206

1.338 1.312 1.289 1.270 1.252 1.412 1.385 1.361 1.340 1.321 I.465 1.438 1.414 1.392 1.373 1.511 I.484 1.460 I.438 I.419 1.552 1.526 1.502 I. 481 1.461 1.589 1.564 1.542 1.521 I.502 1.625 1.601 1.580 1.561 1.542 1.659 1.638 1.618 1.599 1.581 I.693 1.673 1.655 1.638 1.622

Values calculated after method of (40).

4. WATER - CARBON DIOXIDE MIXTURES (12) and (41).

4.1 Volume 4.2 Solvus Volumes of mixtures of water and carbon dioxide are The solvus in the water-carbon dioxide system has been

presented in Table 13a-d from 300” to 800°C and 50 bars determined by (37), (38) and (36). The more recent work to 6 Kbars, for mole fractions of carbon dioxide of 0.2, of (36) most closely matches that of (38), although some 0.4, 0.6 and 0.8. Data are taken from (36), (13), (14), departures are noted. Although (36) does not include tab-

66 H,O-CO, FLUIDS

TABLE 13a. Volume of Water-Carbon Dioxide Mixtures, cm3/mole, Xc02= 0.2 Pbars/T’C 400 4.50 500 550 600 650 700 750 800 50 1254. 1342. 1417. 1506. 1600. 1674. 1730. 100 150 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000

562.0 316.0 358.5 214.0 252.5 151.0 193.5 115.0 151.0

125.4 75.0 103.0

90.4 57.0 79.0 53.0 60.0

53.2 48.2

611.5 396.4 289.0 227.0 178.0 149.0 126.9 108.0 91.0 76.0 62.2 56.5 52.4

657.0 428.8 314.9 246.7 201.4 169.1 145.1 126.5 111.8

71.7 63.5 58.1 54.3

700.7 461.2 341.0 268.7 220.6 186.4 160.9 141.4 126.1 96.2 82.0 72.5 64.8 59.9 52.8

745.2 491.6 365.1 289.3 238.8 202.8 175.9 155.1 138.4 107. 91.8 80.3 71.5 65.2 56.2 50.4

792.2 523.4 389.2 308.9 255.5 217.5 189.1 167.2 149.7 118. 101. 87.7 78.4 71.2 61.0 55.1 50.4

834.5 868.2 554.5 579.6 414.3 434.6 330.2 347.2 274.1 288.8 234.0 247.1 204.1 215.8 180.9 191.5 162.5 172.1 127. 108. 94.8 84.8 77.0 64.7 57.5 52.8

29.31 33.00 37.37 42.33 26.46 28.93 31.57 34.34 24.92 26.81 28.71 30.58 23.88 25.41 26.88 28.25 23.08 24.37 25.54 26.59

Values from (36). (13), (14). (f2), (41).

TABLE 13b. Volume of Water-Carbon Dioxide Mixtures, cm3/mole, Xco2= 0.4 Pbars/TOC 300 400 450 500 550 600 650 700 750 50 1256. 1348. 1415. 1510. 1604. 1669. 100 150 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000

336.0 238.0 180.0 148.0

107.0

56.96 83.0 50.44 72.0 46.17 58.0 43.44 53.0 41.18 49.4 39.74

578.5 375.0 271.5 213.0 171.0 147.7 127.0 113.2 100.0 80.0 67.3 61.3 56.8 53.2

800 1728.

621.5 409.3 303.0 243.5 195.0 167.0 144.8 127.5 112.0 93.0 75.5 67.8 62.7 58.8 52.9

667.6 441 .o 327.9 260.3 215.4 183.5 159.8 141.5 127.0

83.7 74.1 67.8 63.3 57.0 52.8 49.6

706.8 470.0 351.3 279.9 232.4 198.6 173.5 154.3 139.3 106. 91.4 81.3 73.8 68.5 61.1 55.5 51.3

36.19 40.27 44.85 31.92 34.68 37.56 29.84 31.98 34.11 28.45 30.20 31.88 27.30 28.76 30.13

751.8 499.5 373.7 298.4 248.4 212.8 186.2 165.6 149.2 115. 100. 88.6 80.3 74.4 64.6 58.7 54.2 50.7

799.4 531.3 397.5 317.4 264.2 226.3 198.0 176.1 158.7 124. 106. 94.8 85.5 78.7 68.8 61.8 56.6 53.0 49.84 40.52 36.21 33.48 31.38

837.3 874.2 559.8 587.6 420.9 443.3 337.5 356.1 281.9 297.6 242.3 255.8 212.6 224.4 189.6 200.1 171.3 180.7 133. 114. 101. 91.4 83.7 72.3 65.0 59.0 54.8 51.0

Values from (36), (13). (14), (12) and (41).

BOWERS 67

TABLE 13~. Volume of Water-Carbon Dioxide Mixtures, cm3/mole, Xcoz= 0.6 PbarslT’C 300 400 450 500 550 600 650 700 750 800

50 937.75 1256. 1352. 1420. 1517. 1606. 1671. 1736.

100 150 200 250

300 350 400 450 500

600 700 800 900 1000

1200 1400 1600 1800 2000 3000 4000 5000 6000

463.66

280.18 352.0 193.32 257.0 161.28 201.0 129.58 173.0 108.01 93.81 127.0 84.36 76.52 104.0 66.14 87.0 59.58 71.2

54.96 64.5 51.33 60.4 48.83 57.1

52.7 48.8

592.5

388.0 286.0 227.0

187.0 162.4 142.5 127.6 115.5 95.0 79.0 71.7

66.5 62.5

56.6 52.4 48.8

627.8 418.0

314.0 252.0 207.0 180.0 157.7 141.0 127.0 107.0 88.2 78.7

72.1 67.5 61.1 56.0 53.0 50.4 47.12 40.04 36.67 34.41 32.50

675.0 449.7

337.3 270.2 225.7 194.1 170.6 152.6 138.3

42.69 37.01 34.31 32.49

30.90

96.6 86.4 78.3

72.5 64.4 59.6 55.6 52.5 50.0

714.5

478.6 360.4

289.4 242.2 208.6 183.7 164.6 149.8 119.

105. 93.5 84.7

78.4 69.0 62.7 58.1 54.4 51.98 43.23 39.10 36.38 34.13

759.4 507.4

381.8 306.7 256.9 221.5 195.1 174.8 158.6 127. 111.

98.8 89.5 82.9

72.9 65.8 60.9 56.7 53.7

805.1 538.3

405.1 325.4 272.4 234.7 206.6 184.8 167.4 134. 117. 104.

94.4 87.4 76.9

68.8 63.7 59.3 57.20 46.56 41.61 38.38

35.78

842.5 882.7

566.0 595.7 427.5 450.9

344.3 363.3 288.9 304.6 249.3 262.6 219.7 231.3 196.8 207.1 178.6 188.0 142. 122. 110. 99.2

91.9 79.4 71.7 65.4 61.0

Values from (36), (13), (14). (12) and (41).

TABLE 13d. Volume of Water-Carbon Dioxide Mixtures, cm3/mole, Xco2= 0.8 Pbars/TOC 300 400 450 500 550 600 650 700 750

50 943.58 1265. 1361. 1434. 1530. 1606. 1683.

800

1750.

100 150 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 1800 2000

3000 4000 5000 6000

460.58 305.05 224.46 178.79 147.64 127.93 111.71 101.05 92.22 79.72 71.80 65.87 60.95 58.08

365.0 270.0 217.0 182.0

140.0

113.0 100.0 84.7 77.0 70.9 66.6 60.2 56.0 52.8 50.1 48.58

41.73 38.34 36.01

34.02

600.0 397.5 297.0 237.0 199.0 173.6 153.0 137.8 125.0 107.0 91.9 82.7 76.8 71.5 64.6 59.7 56.0

53.1 49.9

635.8 425.9 323.5 259.5 216.0 189.0 166.7

151.0 135.0 115.0 99.2 90.0 82.8 77.1 69.1 63.4 59.5

56.1 53.33 44.97

40.86 38.06 35.73

683.2 457.6 345.2 278.0 233.6 202.1 178.8 160.8 146.7 122. 107. 96.7 88.2 82.1 73.0 66.5 62.0

58.6 55.8

724.8 487.8

369.1 297.8 250.4 216.7 191.7 172.6 157.8 129. 114. 103. 93.6 87.1 76.8 69.5 64.4

60.5 58.37 48.40 43.53

40.24 37.55

768.7 515.7

389.6 314.3 264.5 229.1 202.9 182.6 166.5 136. 121. 108. 98.9 92.1 80.6 72.9 67.2 63.1

59.5

809.4 544.3 412.1 332.9 280.2 242.7 214.8 193.1 175.9 143. 126. 113. 103. 95.5 84.3 76.3 70.3 65.6

63.70 51.99 46.32

42.52 39.46

851.0 891.2 573.4 602.4 434.4 456.6 350.9 368.6 295.3 309.7 255.6 267.8 225.8 236.7 202.8 212.9 184.4 194.5 150. 131. 118. 108. 99.5 87.9 79.6 72.8 68.1

Values from (36), (13). (14), (12) and (41).

68 H20-CO, FLUIDS

ulations of the solvus composition, Table 14 reproduces values taken visually from their graphs.

4.3 Dielectric Constant The addition of CO> to H,O affects the electrostatic prop-

erties of the solution and subsequently influences ion association and mineral solubilities. It is useful to know the effect of CO, on the dielectric constant of H,O because this information can be used to estimate how ion association constants change in H,O-CO, mixtures by assuming, as for pure HzO, that ion association constants do not vary along isopleths of the dielectric constant.

Dielectric constants of water-carbon dioxide mixtures have not been measured, but they can be calculated from the dielectric constants of pure water and carbon dioxide following the approach of (27) as outlined by (40):

where V, is the volume fraction of water in the solution. Calculated dielectric constants for water-carbon dioxide mixtures are presented in Table 15a-d from 400” to 1000°C and 50 bars to 10 Kbars, for mole fractions of carbon dioxide of 0.2, 0.4, 0.6 and 0.8.

5. EQUATIONS OF STATE

5.1 Water 5.2 Carbon Dioxide Equations of state for water that are commonly used Equations of state for carbon dioxide in common use

include those by (16), (10) and (15). The equation by (16) covers a pressure-temperature range to 10 Kbar and from 25” to 900°C. This work is extended by (10) to pressures of 100 Kbar. The EOS proposed by (15) is valid to 2000°C and 30 Kbar. Recently, new EOS for water based on the work of (26) have been proposed by (34), (17) and (19). These EOS give thermodynamic functions for water with smooth transitions between the critical point and far from the critical region. The EOS presented by (17) is tested to 10 Kbar and lOOO”C, although the author states that it may be extrapolated to 250 Kbar and 2000°C. The work by (19) concentrates on the critical region, with equations describing fluid properties from 200 to 450 bars and 350” to 475°C. The EOS given by (34) covers the entire fluid region where data exist and can be used to 1000°C and 250 Kbar. This equation fits the high pressure data better than the equations of (15) and (17). EOS for water to higher temperatures and pressures have also been devel- oped from the method of molecular dynamics. (7) presents a molecular dynamics study tested over the pressure-temperature range from 0.5 to 40 Kbars and 25” to 2100°C. Use of this equation by the authors to predict water volumes at 300 Kbars results in predictions which deviate by less than 10% from the volume results of shock-wave experi- merits. An additional molecular dynamics study by (4) yields an EOS for water from 5 to 1000 Kbar and approximately 500” to 3700°C.

TABLE 14. The H,O-CO, Solvus, Mole Fraction CO, TEMP, OC 500 bars 1000 bars 1500 bars

X(CO,)liq WO+v X(CO,)liq X(C02)vap X(CO,)liq WC02)vap 230 .87 .86 .82 240 .84 .80 .08 .77 250 .78 .74 .12 .72 260 - .71 .08 .68 .16 .66 270 .65 .12 .62 .23 .56

280 .59 .17 .49 290 .54 300 .08 .47 310 .I8 .34

TEMP, “C 2000 bars 2500 bars 3000 bars

230

X(CO,)liq WC02)w .80

X(CO,)liq WC02)w .81

X(CO,)liq WQ)vap .86

240 .07 .76 .13 .77 .13 .80

250 .15 .71 .15 .73 .13 .73 260 .20 .66 .18 .67 .14 .68

270 .26 .51 .17 .55 Values from (36).

BOWERS 69

TABLE 15a. Dielectric Constant of Water-Carbon Dioxide Mixtures, Xcoz= 0.2 Pbars/T’C 400 500 600 700 800 900 1000

50 1.090 1.066 1.050 1.042 1.034 1.026 1.026 100 1.139 1.093 1.069 1.084 1.068 1.060 1.052 200 I.464 I.256 I.182 I.189 1.150 I. 126 1.110 300 2.948 1.508 1.327 1.306 1.238 1.199 1.168 400 4.064 1.910 1.526 1.440 I.346 1.279 1.232 500 4.772 2.476 1.776 I.596 1.451 1.363 1.296 600 5.377 3.119 2.083 I.772 1.574 1.454 1.373 700 5.902 3.706 2.425 I.954 1.699 1.549 1.449 800 6.354 4.200 2.777 2.154 1.835 1.649 1.524 900 6.744 4.624 3.129 1000 7.091 4.984 3.469 2.565 2.121 1.864 1.690 1200 7.690 5.593 4.069 1400 8.209 6.096 4.580 2000 9.390 7.226 5.683 4.252 3.446 2.898 2.516 3000 10.757 8.502 6.873 5.351 4.429 3.742 3.233 4000 11.739 9.397 7.659 6.137 5.155 4.399 3.820 5000 12.539 10.101 8.255 6.776 5.744 4.945 4.319 6000 13.222 10.694 8.726 7000 13.822 11.206 9.113 8000 14.367 11.651 9.441 9000 14.855 12.062 9.710 10000 15.314 12.421

Values calculated after method of (40). 9.944

TABLE 15b. Dielectric Constant of Water-Carbon Dioxide Mixtures, XcO,= 0.4 Pbars/T’C 400 500 600 700 800 900 1000

50 1.071 1.053 1.041 1.034 1.028 1.022 1.022 100 1.110 1.076 1.058 1.069 1.056 1.049 1.043 200 1.330 1.199 1.146 1.151 1.121 1.104 1.091 300 1.978 1.371 1.253 1.239 1.190 1.161 1.137 400 2.409 1.615 1.391 1.335 1.270 1.222 1.18s 500 2.738 1.917 1.552 1.444 1.347 1.286 1.237 600 3.037 2.229 1.739 1.560 1.433 1.351 1.295 700 3.306 2.505 1.936 I.677 1.519 1.420 1.351 800 3.542 2.740 2.129 1.800 1.610 1.490 1.406 900 3.746 2.946 2.316 1000 3.931 3.123 2.492 2.043 1.793 1.636 1.52-l 1200 4.252 3.429 2.799 1400 4.536 3.688 3.059 2000 5.181 4.281 3.620 2.958 2.558 2.266 2.049 3000 5.931 4.964 4.248 3.544 3.098 2.747 2.47-f 4000 6.465 5.445 4.670 3.964 3.491 3.111 2. SOS 5000 6.902 5.831 5.000 4.312 3.815 3.417 3.094 6000 7.278 6.164 5.272 7000 7.611 6.456 5.503 8000 7.920 6.715 5.708 9000 8.197 6.961 5.883 10000 8.464 7.181


70 H,O-CO, FLUIDS

TABLE 1%. Dielectric Constant of Water-Carbon Dioxide Mixtures, Xcc,= 0.6 Pbars/T”C 400 500 600 700 800 900 1000 50 1.053 1.040 1.032 1.027 1.022 1.018 1.01s 100 1.083 1.060 1.047 1.054 1.044 1.039 I.035 200 1.225 1.148 1.113 1.114 1.094 1.082 1.072 300 1.525 1.260 1.189 1.178 1.145 1.125 I.108 400 I.720 I.402 1.279 I.244 I. 202 I.170 I.I‘A5 500 I.885 1.561 1.378 1.316 1.255 1.215 1.183 600 2.037 1.716 1.487 1.389 1.313 1.261 1.221 700 2.175 1.851 1.597 1.461 1.369 1.308 1.26d 800 2.296 1.968 1.701 1.534 1.427 1.355 1.303 900 2.401 2.072 1.800 1000 2.497 2.162 1.891 1.674 1.541 1.450 1.383 1200 2.664 2.320 2.050 1400 2.812 2.454 2.185 2000 3.149 2.764 2.474 2.171 1.976 1.826 1.707 3000 3.539 3.124 2.808 2.487 2.273 2.099 1.95; 4000 3.816 3.377 3.034 2.712 2.488 2.301 2.14-S 5000 4.044 3.583 3.216 2.902 2.668 2.474 2.312 6000 4.240 3.763 3.370 7000 4.414 3.923 3.503 8000 4.579 4.065 3.625 9000 4.726 4.204 3.733 10000 4.869 4.329

Values calculated atier method of (40). 3.837

TABLE 15d. Dielectric Constant of Water-Carbon Dioxide Mixtures, Xc,,,= 0.8 Pbars/T“C 400 500 600 700 800 900 1000

50 1.035 1.027 1.023 1.019 1.017 1.014 I.014 100 1.059 1.045 1.037 1.039 1.033 1.030 1.027 200 1.141 1.103 1.083 1.080 1.068 1.060 1.054 300 1.270 1.168 1.131 1.122 1.103 1.091 1.081 400 1.359 1.242 1.184 1.164 1.140 1.122 1.108 500 1.438 1.319 1.239 1.207 1.175 1.152 1.133 600 1.512 1.390 1.296 1.249 1.210 1.181 1.160 700 1.580 1.454 1.352 1.289 1.243 1.211 1.187 800 I. 639 1.509 1.404 1.330 1.278 1.240 1.212 900 1.689 1.560 1.452 1000 1.736 1.603 1.496 1.405 1.342 1.297 1.262 1200 1.817 1.681 1.573 1400 1.889 1.747 1.640 2000 2.051 1.900 1.783 1.661 1.576 1.507 1.450 3000 2.238 2.078 1.952 1.824 1.733 1.655 1.590 4000 2.371 2.204 2.069 1.940 1.846 1.764 1.695 5000 2.480 2.307 2.165 2.040 1.942 1.858 1.787 6000 2.574 2.398 2.248 7000 2.658 2.480 2.322 8000 2.738 2.554 2.391 9000 2.809 2.626 2.454 10000 2.880 2.692


BOWERS 71

include those by (6) and (35). (6) gives an equation for the thermodynamic properties of carbon dioxide from -50” to 1000°C and from 1 bar to 10 Kbars. Their equation is a version of the Redlich Kwong EOS for CO, (9), which was fit by (9) to experimental density data for carbon dioxide from 0” to 800°C and pressures up to 1400 bars. Several other modified Redlich Kwong EOS exist for CO,. (35) presents an equation for carbon dioxide volumes from 2 to 10 Kbars and 100” to 1000°C. More recently, (29) have presented an EOS for carbon dioxide obtained by fitting parameters not only to PVT data, but also to phase equilibrium data. They report that this equation is reliable in the range of 1 bar to 42 Kbars, and approximately 200” to 1500°C. Molecular dynamic studies yield an EOS by (5) over a pressure-temperature range from 5 to 1000 Kbar and approximately 200” to 3700°C.

5.3 Water - Carbon Dioxide Mixtures A recent summary of EOS for H,O-CO, mixtures (30)

provides information for a large number of EOS, however the EOS currently in most common use for H,O-CO, mixtures include that by (18) as modified by (1 l), and that by (22). The former (18, 11) EOS is modified after the work of (9), and can be used to 700°C and several Kbars. (22) apply their EOS from 400” to 800°C and from 500 bars to 30 Kbar.

Acknowledgments: I would like to thank Mike Sterner, Bob Bodnar, and John Tanger for their helpful advice, Kim Reynolds for help with the tables, and John Brodholt for his aid in supplying calculations for some of the shock experiment information. I also thank John Brodholt and Mike Sterner for their constructive re- views of the manuscript.

1.

2.

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4.

5.

6.

7.

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Presure-Volume-Temperature Properties of H2O-CO2 Fluids (Geophysics) [Short Article] - T. Bowers...

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