Appendix D—
Conversion Factors, Steam Properties, and Conversion of Geothermal Heat to Electricity
Conversion Factors
Conversion factors shown in Table D.1 are presented as basic equivalents in English, cgs (centimeter/gram/second), and SI (International System) units to facilitate computations in volcanological and mechanical engineering models.
Thermodynamic Properties of Steam
Throughout this book, heat flow through rocks and heat transfer to water are discussed as important concepts to consider when attempting to understand volcanic and hydrothermal behavior. Although water is not pure in volcanic hydrothermal systems and contains variable amounts of dissolved gases, ionic species, and molecular species, it is possible to estimate the pressure/volume relationships of fluids on a first-order approximation by considering the phase relationships of pure water. We recommend using the U.S. National Bureau of Standards steam tables (Haar et al ., 1984), which are published in SI units for temperatures between ambient (273 K) and 1273 K at pressures from atmospheric (0.1 MPa) to 1500 MPa (15 kbar). The quick-reference table in this appendix (Table D.2) lists values for some of these conditions.
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Table D.1. Basic Equivalents for Major Measurement Systems | Unit | English | cgs | SI | Length | 1.0 in. | 2.54000 cm | 0.02540000 m | Mass | 1.0 lb | 453.59237 g | 0.45359237 kg | Temperature | 212.0°F | 100.0°C | 373.0 K | Force | 1.0 lbf | 453.59237 gf
444,822.2 dynes | 0.45359237 kgf
4.448222 N | Pressure
(1 atma ) | 1.0 bar
14.696 lb/ft2 | 1,000,000.00 dynes/cm2
1,013,250.00 dynes/cm2 | 100,000.0 Pa
101,325.0 Pa | Energy | 1.0 Btu | 1.054 × 1010 ergs | 1054.350 J
0.292875 W-hr | | | 1.0 kt | 4.184 × 1019 ergs | 1.1626 × 106 kW-hr | Work | 1.0 ft/lb | 0.32405 g-cal | 1.355818 J | Power | 1.0 Btu/hr
1.0 hp | 0.0699988 g-cal/s
178.2263 g-cals/s | 0.292875 W
745.6999 W | Specific heat and
specific entropy | 1.0 Btu/lb-°R | 1.0 cal/g-°C | 4.184 kJ/kg-K | Specific volume | 1.0 ft3 /lb | 62.428 cm3 /g | 0.06248 m3 /kg | a At sea level. | | | |
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Conversion of Geothermal Heat to Electricity
Production of electricity from a geothermal heat source is limited by the Second Law of Thermodynamics, which specifies that it is impossible to convert all the heat energy from a system into mechanical—hence, electrical—energy (Gokcen, 1975). For an idealized geothermal power conversion process, the total maximum work that can be extracted from a geothermal fluid is often termed availability (B), which is given by
where D H and D S are the enthalpy and entropy differences between ambient conditions and the geothermal fluid's wellhead pressure and temperature; Ta = ambient temperature. Figure D.1 (a) is a plot of D B as a function of wellhead temperature for saturated vapor and saturated liquid cooled to three different ambient temperatures. The actual amount of work converted to electrical power (Wnet ) is a function of the cycle efficiency of the power plant (hc )
Figure D.1 (b) shows typical cycle efficiencies for geothermal plants as a function of wellhead temperature for a range of condensing temperatures. The discarded or reinjected fluids above ambient temperatures are not counted as thermodynamic losses in calculations of cycle efficiency; thus hc can be proportionately larger than the utilized efficiency for some applications (Tester, 1982).
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Fig. D.1
(a) Plot of D B as a function of wellhead temperature
for saturated vapor and saturated liquid that have
cooled to three different ambient temperatures.
(b) Typical cycle efficiencies for geothermal plants
are shown as a function of wellhead temperature
for a range of condensing temperatures.
(Adapted from Tester, 1982.)
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Table D.2. Abbreviated Steam Tablea | Temperature (°C) | Density
(kg/m3 ) | Enthalpy (kJ/kg) | Entropy (kJ/kg-K) | Heat Capacity (kJ/kg-K) | Isentropic Coefficient | 1.0 Bar | | | | | | 0.0 | 999.83 | 0.06 | -0.00015 | 4.228 | | 99.6 (I) | 958.66 | 417.51 | 1.30273 | | | 99.6 (v) | 0.5902 | 2675.1 | 7.3589 | | | 100 | 0.5896 | 2675.9 | 7.3609 | 2.042 | 1.33 | 200 | 0.46035 | 2874.8 | 7.8335 | 1.975 | 1.31 | 300 | 0.37896 | 3073.9 | 8.2152 | 2.013 | 1.30 | 400 | 0.32230 | 3278.0 | 8.5432 | 2.070 | 1.29 | 500 | 0.28046 | 3488.2 | 8.8342 | 2.135 | 1.28 | 600 | 0.24827 | 3705.0 | 9.0979 | 2.203 | 1.27 | 700 | 0.22272 | 3928.8 | 9.3405 | 2.273 | 1.26 | 800 | 0.20194 | 4159.7 | 9.5662 | 2.343 | 1.25 | 900 | 0.18472 | 4397.5 | 9.7781 | 2.412 | 1.24 | 1000 | 0.17020 | 4642.0 | 9.9781 | 2.478 | 1.23 | 25.0 Bar | | | | | | 0 | 1001.05 | 2.51 | 0.00003 | 4.215 | | 100 | 959.52 | 420.87 | 1.30502 | 4.211 | | 200 | 865.47 | 852.76 | 2.32926 | 4.484 | | 224.0 (I) | 835.19 | 961.97 | 2.55438 | | | 224.0 (v) | 12.508 | 2802.2 | 6.2560 | | | 300 | 10.113 | 3008.0 | 6.6424 | 2.433 | 1.29 | 400 | 8.327 | 3239.2 | 7.0146 | 2.245 | 1.29 | 500 | 7.144 | 3462.2 | 7.3235 | 2.228 | 1.28 | 600 | 6.287 | 3686.3 | 7.5960 | 2.259 | 1.27 | 700 | 5.608 | 3914.7 | 7.8436 | 2.310 | 1.26 | 800 | 5.071 | 4148.6 | 8.0724 | 2.370 | 1.25 | 900 | 4.6305 | 4388.7 | 8.2862 | 2.431 | 1.24 | 1000 | 4.2616 | 4634.9 | 8.4876 | 2.493 | 1.23 | 50.0 Bar | | | | | | 0 | 1002.31 | 5.05 | 0.00020 | 4.202 | 400 | 100 | 960.68 | 422.75 | 1.3038 | 4.206 | 450 | 200 | 867.35 | 853.79 | 2.32533 | 4.469 | 250 | 264.0 (I) | 777.52 | 1154.20 | 2.92011 | | | 264.0 (v) | 25.355 | 2793.7 | 5.9725 | | | 300 | 22.073 | 2923.5 | 6.2067 | 3.181 | 1.28 | 400 | 17.299 | 3195.5 | 6.6456 | 2.468 | 1.28 | 500 | 14.586 | 3433.9 | 6.9760 | 2.335 | 1.28 | 600 | 12.709 | 3666.2 | 7.2586 | 2.322 | 1.27 | 700 | 11.299 | 3899.7 | 7.5117 | 2.351 | 1.26 | 800 | 10.189 | 4137.0 | 7.7438 | 2.398 | 1.25 | 900 | 9.287 | 4379.4 | 7.9598 | 2.452 | 1.24 | 1000 | 8.536 | 4627.4 | 8.1626 | 2.508 | 1.24 |
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D.2. Abbreviated Steam Table (cont.) | Temperature (°C) | Density
(kg/m3 ) | Enthalpy (kJ/kg) | Entropy (kJ/kg-K) | Heat Capacity (kJ/kg-K) | Isentropic Coefficient | 74.0 Bar | | | | | | 0 | 1003.52 | 7.48 | 0.00033 | 4.190 | 250 | 100 | 961.79 | 424.56 | 1.30123 | 4.200 | 250 | 200 | 869.13 | 854.80 | 2.32162 | 4.456 | 225 | 289.6 (l) | 732.83 | 1287.24 | 3.15622 | | | 289.6 (v) | 38.892 | 2766.4 | 5.7845 | | | 300 | 36.713 | 2817.5 | .8744 | 4.642 | 1.27 | 400 | 26.665 | 3150.0 | 6.4128 | 2.736 | 1.28 | 500 | 22.041 | 3405.7 | 6.7674 | 2.448 | 1.28 | 600 | 19.036 | 3646.5 | 7.0604 | 2.386 | 1.27 | 700 | 16.843 | 3885.0 | 7.3190 | 2.392 | 1.26 | 800 | 15.145 | 4125.7 | 7.5544 | 2.425 | 1.25 | 900 | 13.780 | 4370.5 | 7.7725 | 2.472 | 1.24 | 1000 | 12.652 | 4620.3 | 7.9767 | 2.523 | 1.24 | 100.0 Bar | | | | | | 0 | 1004.81 | 10.10 | 0.00045 | 4.177 | 200 | 100 | 962.98 | 426.52 | 1.29924 | 4.195 | 225 | 200 | 871.03 | 855.91 | 2.31766 | 4.442 | 170 | 300 | 715.58 | 1342.38 | 3.24697 | 5.675 | 60 | 311.0 (l) | 688.63 | 1407.28 | 3.35912 | | | 311.0 (v) | 55.48 | 2724.5 | 5.6139 | | | 400 | 37.867 | 3096.1 | 6.2114 | 3.100 | 1.28 | 500 | 30.503 | 3374.0 | 6.5971 | 2.584 | 1.28 | 600 | 26.068 | 3624.7 | 6.9022 | 2.458 | 1.27 | 700 | 22.941 | 3869.0 | 7.1671 | 2.437 | 1.26 | 800 | 20.982 | 4112.5 | 7.3963 | 2.456 | 1.26 | 900 | 19.050 | 4360.1 | 7.6169 | 2.494 | 1.25 | 1000 | 17.466 | 4612.0 | 7.8229 | 2.540 | 1.24 | 150.0 Bar | | | | | | 0 | 1007.28 | 15.11 | 0.00060 | 4.153 | 150 | 100 | 965.25 | 430.29 | 1.29546 | 4.184 | 160 | 200 | 874.6 | 858.1 | 2.3102 | 4.41 | 110 | 300 | 725.9 | 1337.4 | 3.2261 | 5.470 | 45 | 342.2 (l) | 603.5 | 1609.8 | 3.6837 | | | 342.2 (v) | 96.72 | 2610.1 | 5.3092 | | | 400 | 63.89 | 2974.7 | 5.8799 | 4.177 | 1.28 | 500 | 48.08 | 3309.3 | 6.3452 | 2.891 | 1.29 | 600 | 40.15 | 3581.5 | 6.6767 | 2.610 | 1.28 | 700 | 34.94 | 3837.6 | 6.9544 | 2.529 | 1.27 | 800 | 31.12 | 4089.6 | 7.2009 | 2.518 | 1.26 | 900 | 28.15 | 4342.2 | 7.4260 | 2.538 | 1.26 | 1000 | 25.75 | 4597.7 | 7.6350 | 2.573 | 1.25 |
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Table D.2. Abbreviated Steam Table (cont.) | Temperature (°C) | Density
(kg/m3 ) | Enthalpy (kJ/kg) | Entropy (kJ/kg-K) | Heat Capacity (kJ/kg-K) | Isentropic Coefficient | 200.0 Bar | | | | | | 0 | 1010.21 | 21.08 | 0.00066 | 4.130 | 100 | 100 | 967.92 | 434.83 | 1.29098 | 4.174 | 125 | 200 | 878.7 | 860.9 | 2.3015 | 4.394 | 90 | 300 | 735.0 | 1333.4 | 3.2073 | 5.311 | 40 | 365.8 (I) | 491.2 | 1826.7 | 4.0146 | | | 365.8 (v) | 170.25 | 2413.6 | 4.9330 | | | 400 | 100.54 | 2816.9 | 5.5521 | 6.371 | 1.29 | 500 | 67.71 | 3239.4 | 6.1417 | 3.269 | 1.30 | 600 | 55.04 | 3536.7 | 6.5039 | 2.778 | 1.29 | 700 | 47.32 | 3805.5 | 6.7955 | 2.627 | 1.28 | 800 | 41.87 | 4065.4 | 7.0498 | 2.583 | 1.27 | 900 | 37.72 | 4323.5 | 7.2797 | 2.583 | 1.26 | 1000 | 34.42 | 4582.8 | 7.4919 | 2.606 | 1.26 | 300.0 Bar | | | | | | 0 | 1014.53 | 29.92 | 0.00051 | 4.089 | 70 | 100 | 971.86 | 441.64 | 1.28439 | 4.154 | 80 | 200 | 884.7 | 865.2 | 2.2890 | 4.350 | 60 | 300 | 750.9 | 1328.0 | 3.1744 | 5.075 | 25 | 400 | 358.05 | 2150.7 | 4.4723 | 25.080 | 2 | 500 | 115.26 | 3083.5 | 5.7936 | 4.312 | 1.34 | 600 | 87.48 | 3443.1 | 6.2324 | 3.160 | 1.32 | 700 | 73.23 | 3740.1 | 6.5547 | 2.836 | 1.31 | 800 | 63.92 | 4016.7 | 6.8254 | 2.716 | 1.29 | 900 | 57.13 | 4285.9 | 7.0653 | 2.677 | 1.28 | 1000 | 51.87 | 4553.3 | 7.2840 | 2.674 | 1.27 | 400.0 Bar | | | | | | 0 | 1019.23 | 39.63 | 0.00003 | 4.053 | 60 | 100 | 976.12 | 449.24 | 1.27722 | 4.135 | 70 | 200 | 891.0 | 870.1 | 2.2758 | 4.312 | 45 | 300 | 764.6 | 1324.8 | 3.1457 | 4.906 | 25 | 400 | 523.7 | 1930.8 | 4.1134 | 8.717 | 5 | 500 | 177.97 | 2906.7 | 5.4745 | 5.799 | 1.45 | 600 | 123.81 | 3345.8 | 6.0111 | 3.597 | 1.37 | 700 | 100.71 | 3673.8 | 6.3673 | 3.057 | 1.34 | 800 | 86.68 | 3967.8 | 6.6551 | 2.854 | 1.31 | 900 | 76.86 | 4248.5 | 6.9052 | 2.771 | 1.30 | 1000 | 69.44 | 4523.9 | 7.1305 | 2.743 | 1.29 |
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Table D.2. Abbreviated Steam Table (cont.) | Temperature (°C) | Density
(kg/m3 ) | Enthalpy (kJ/kg) | Entropy (kJ/kg-K) | Heat Capacity (kJ/kg-K) | Isentropic Coefficient | 500.0 Bar | | | | | | 0 | 1023.82 | 49.20 | -0.00076 | 4.021 | 45 | 100 | 980.27 | 456.84 | 1.27021 | 4.117 | 55 | 200 | 897.0 | 875.3 | 2.2631 | 4.277 | 40 | 300 | 776.6 | 1323.1 | 3.1202 | 4.775 | 22 | 400 | 578.0 | 1874.1 | 4.0022 | 6.789 | 7 | 500 | 257.0 | 2724.2 | 5.1780 | 7.239 | 1.8 | 600 | 163.99 | 3247.7 | 5.8184 | 4.062 | 1.45 | 700 | 129.64 | 3607.8 | 6.2097 | 3.283 | 1.37 | 800 | 110.09 | 3919.5 | 6.5148 | 2.992 | 1.34 | 900 | 96.88 | 4211.5 | 6.7751 | 2.866 | 1.32 | 1000 | 87.12 | 4495.0 | 7.0070 | 2.812 | 1.31 | 1,000.0 Bar | | | | | | 0 | 1045.31 | 95.40 | -0.00854 | 3.909 | 30 | 100 | 999.70 | 495.00 | 1.23713 | 4.139 | 35 | 200 | 923.7 | 903.6 | 2.2068 | 4.141 | 25 | 300 | 823.2 | 1328.2 | 3.0202 | 4.391 | 15 | 400 | 692.6 | 1790.9 | 3.7632 | 4.911 | 8 | 500 | 528.2 | 2316.2 | 4.4897 | 5.557 | 4 | 600 | 373.9 | 2863.4 | 5.1558 | 5.123 | 2.5 | 700 | 282.4 | 3323.1 | 5.6552 | 4.129 | 1.75 | 800 | 231.03 | 3704.3 | 6.0286 | 3.561 | 1.55 | 900 | 198.45 | 4044.3 | 6.3317 | 3.269 | 1.45 | 1000 | 75.61 | 4362.6 | 6.5921 | 3.113 | 1.42 | a Temperature and pressure units shown as bar and Celsius scales, respectively, to correspond to tabulated tables from Haar et al . (1984). Values denoting liquid (I) and vapor (v) saturation are shown in bold. Isentropic (expansion) coefficients are approximated from graphical data in Fig. 7 of Haar et al . (1984). |
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