1、Energy Functions for Gaseous C02-H20 Mixtures Mukund R. Patel James C. Holste Kenneth R. Hall Philip T. Eubank Department of Chemical Engineering Texas A and for the infringement of any patent or the violation of any federal, state or municipal law or regula- tion arising from the use of, any inform
2、ation, apparatus, method or process disclosed in this report. i GPA TP-14 87 3824b99 0011449 bbL FOREWORD Thennophysical properties of the carbon dioxide/water system have long been important in geological studies. have been used for enhanced oil recovery in Texas and Oklahoma oil fields. Recently,
3、large amounts of carbon dioxide Much of this carbon dioxide is produced in Colorado and moved via pipeline to its final destination. The removal of water from carbon dioxide prior to pipelining to prevent the formation of a condensed phase at elevated pressures relies upon the properties shown in TP
4、-14. While the primary support for this research came from the National Science Foundation, the experimental techniques and calculational methods were developed under GPA Research Project #772, a similar study of wet natural gas systems. authors have expressed their appreciation to the GPA Enthalpy
5、Committee for its technical advice and support during the past 10 years. The OXY % Car B. Sutton, GPA Secretary ii GPA TP-14 87 3824677 OOL1450 383 1 ENERGY FUNCTIONS FOR GASEOUS CO2-H2O MIXTURES A tabulation of total energy properties derived from experimental data for mixtures of 2% 5%, lo%, 25%,
6、and 50% H20 in CO2 along with pressure- enthalpy diagrams for the same. Mukund R. Patel, James C. Holste, Kenneth R. Hall, and Philip T. Eubank Department of Chemical Engineering Texas A making an isochoric run (pressure measurements at fixed temperature increments); returning the cell to the origin
7、al condition; and performing an expansion of the sample into a previously evacauted secondary cell volume. A series of such isochoric runs coupled with isothermal expansions, typically at the highest temperature, constitute a B-I surface run. An important feature of the B-l method is that it generat
8、es an entire P-p-T surface with one filling of the sample; hence, for mixtures there is no need to duplicate a composition. Being the only two observables in the B-I experiment, the pressure and temperature are measured with exterme accuracy and precision. Pressure measurements are accurate to 0.01%
9、 and precise to 0.001%, whereas the temperatures are accurate to 10 mK with a precision of 5 mK or better. DATA REDUCTION TO ENERGY FUNCTIONS Analysis of the measured pressures and temperatures for a B-I surface run provides the densities and compressibilitics. However, for systems for which adsorpt
10、ion is diagnosed, corrections for adsorption contributions have to be made independently. GPA TP-14 87 3824699 0011452 i156 H 3 Such was the case for the present COi-HzO mixtures and the data were corrected as described in detail by Patel 114. Once these corrections have been made and the densities
11、and cornpressibilities determined, calculation of the thermodynamic properties is achieved through the use of residual properties. A residual property is defined as the real fluid property value less the perfect gas state property value. Of the various forms of such property changes discussed by Hal
12、l et al. Id, the one discussed here is the real fluid property at the temperature and density of the fluid less the perfect gas property at a reference temperature, Tref, and reference pressure, Pref. Thus, for a property M, the residual property is defined as where the * indicates the hypothetical
13、perfect gas state. integration is: The path chosen for With this formulation, it is most convenient to establish (U - U;,.) and (S - S,Cf), and then to calculate the other properties from these two. The starting equations are and dU=CvT+R - - (lfT),d,p (,“;T), - 1 $ dT T S=Cv-+R - - The residual int
14、ernal energy then is determined using and the residual entropy using (3) GPA TP-14 87 3824677 0011453 O92 4 Finally, the remaining residual properties are calculated from and u - “;er + z re ref = H - H* RT RT T A- A* U- UTef S-SI*, S* R ref = - RT RT R Any reference state may be specified, but for
15、a reference state for which H,“,f and Skf are chosen to equal zero, as is the case here, Gr*ef = O, U* ref = - RTref, and A;ef = - RT,ef. Note that the only integrals required to calculate all the above residual properties are and C; dT JTref R The first two require simple applications of the equati
16、on of state, while the latter two involve only perfect-gas specific heats. Eubank et al. IA show that density data obtained by the B-I method yield the above thermodynamic properties more accurately than do data from either straight Burnett or straight isochoric -measurements. RESULTS Tables 1 throu
17、gh 5 present the total energy properties for the five mixtures. The reference state chosen here is the perfect-gas-state reference of zero enthalpy and entropy at 273.16 K and 1kPa. The perfect-gas specific heats for pure COP were taken from Angus et al. 18 and those for pure H20 were taken from Haa
18、r et a/. 19. The GPA TP-LLi 87 3824699 0011454 T29 5 properties listed have the following estimated accuracies: densities and compressibility factors, 0.05%; internal energies and enthapies, 0.15%; Helmholtz and Gibbs free energies, 0.20%; and entropies, 0.17%. Finally, Figures 1 through 5 give the
19、respective pressure-enthalpy (P-H) diagrams developed from the experimental data. ACKNOWLEDGEMENTS The principal sponsor for this work was the National Science Foundation (Grant CPE 8023182). Additional financial support was provided by the Exxon Research and Engineering Company and by the Gas Proce
20、ssors Association. NOTATION A = Helmholtz free energy C, G = Gibbs free energy H = enthalpy M P = pressure R S = entropy T = absolute temperature U = internal energy Z P = density = specific heat capacity at constant volume = general variable for U, H, A, G, or S = universal gas constant (8.31448 J/
21、mol-K) = compressibility factor (P / pRT) Superscripts * = perfect gas state Su bscripts ref = reference state value 6 LITERATURE CITED 1. Weibe, R., and V. L. Gaddy, “The Solubility in Water of Carbon Dioxide at 50, 75 and 100aCc, at Pressures to 700 Atmospheres“, J. Amer. Chem. Soc., 61, 315 (1939
22、). 2. Weibe, R., and V. L. Gaddy, “The Solubility of Carbon Dioxide in Water at Various Temperatures from 12 to 40” and at Pressures to 500 Atmospheres. Critical Phenomena”, J. Amer. Chem. Soc., 62, 815 (1940). 3. Weibe, R., and V. L. Gaddy, “Vapor Phase Composition of Carbon Dioxide-Water Mixtures
23、at Various Temperatures and at Pressures to 700 Atmospheres”, J. Amer. Chem. Soc, 63, 475 (1941). 4. Houghton, G., A. M, McLean, P. D. Ritchie, “Compressibility, fugacity, and water solubility of carbon dioxide in the region 0-36 atm. and O-100C“, Chem. Eng. Sci., 6, 132 (1957). 5. Coan, C. R., and
24、A. D. King, “Solubility of Water in Compressed Carbon Dioxide, Nitrous Oxide, and Ethane. Evidence for Hydration of Carbon Dioxide and Nitrous Oxide in the Gas Phase”, J. Amer. Chem. Soc., 93, 1857 (1971). 6. Zawisza, A., and B. Malesihska, “Solubility of Carbon Dioxide in Liquid Water and of Water
25、in Gaseous Carbon Dioxide in the Range 0.2-5 MPa and at Temperatures up to 473 K”, J. Chem. Eng. Data, 26, 388 (1981). 7. Hicks, C. P., and C. L. Young, ”The Gas-Liquid Critical Properties of Binary Mixtures” , Chem. Reviews, 75, 119 (1975). 8. Vanderzet, C. E., and N. C. Haas, “Second Cross Viria1
26、Coefficients BI2 for the Gas Mixture (Carbon DioxideSWater) from 300 to 1000 K”, J. Chem. Thermodynamics, 13, 203 (1981). 9. Maass, O., and J. H. Mennie, “Aberrrations from the Ideal Gas Laws in Systems of One and Two Components”, Proc. Royal Soc. London, A-110 198 (1926). 10. Greenwood, H. J., “The
27、 Compressibility of Gaseous Mixtures of Carbon Dioxide and Water Between O and 500 Bars Pressure and 450 and 8OO0C”, Am. 1. Sc., 11. Greenwood, H. J., “Thermodynamic Properties of Gaseous Mixtures of H20 and CO2 Between 450” and 800C and O and 500 Bars”, Am. J. Sc., 273, 561 (1973). 12. Smith, G. R.
28、, and C. J. Wormald, “The Excess Molar Enthalpies of xH20 + (1- x)CO (g) and xH,O. + (l-x)C02 (g)”, J. Chem. Thermodynamics, 16, 543 (1984). 13. Wormald, C. J., C. N. Colling, and G. Smith, “Thermodynamics of Supercritical Steam + Carbon Dioxide Mixtures”, Fluid Phase Equilibria, 10, 223 (1983). 14.
29、 Wormald, C. J., N. M. Lancaster, and A. J. Stllars, ”Excess Enthalpy Experimen- tal Data, Binary Systems: Water+Carbon Monoxide, Water+Carbon Dioxide”, Research Report, RR-83, Gas Processors Assoc., Tulsa, Oklahoma (1985). 15. Patel, M. R., “Thermophysical Properties of Gaseous Carbon Dioxide-Water
30、 Mixtures”, Ph. D. Dissertation, Texas A&M University, College Station, Texas, 267-A, 191 (1969). GPA TP-14 87 3824699 OOL14.56 BTL 7 December (1986). 16. Hall, K. R., P. T. Eubank, and J. C. Holste, “Residual Functions and Fugacity“, Chem. Eng. Education, 124, Summer (1983). 17. Eubank, P. T., K. R
31、. Hall, H. Mansoorian, J. C. Holste, W. R. Lau, and P. J. White, “Accurate Enthalpies from Burnett-lsochoric Density Data“, Proc. 57th Ann. Conv., Gas Processors Association, New Orleans (1978). 18. Angus, S., B. Armstrong, and K. M. de Reuck, “International Thermodynamic Tables of the Fluid State:
32、Carbon Dioxide“, Pergamon Press, Oxford (1973). 19. Haar, L., J. S. Gallagher, and G. S. Kell, “NBS/NRC Steam Tables: Thermo- dynamic and Transport Properties and Computer Programs for Vapor and Liq- uid States of Water in SI Units“, Hemisphere Publishing Corporation, Washing- ton, D. C., (1984). GP
33、A TP-LY 87 E3 3824679 OOLL457 738 8 TABLE 1. TOTAL PROPERTIES FOR THE 98% CO2-2% H2O MIXTURE Pressure Density 2 U H A G 5 MPa mol/m3 kJ/mol kJ/mol kJ/mol kJ/mol kJ/mol-K Temperature = 498.15 K 0.10 24.2 0.9992 4.901 9.040 12.07 16.20 -0.0144 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2.00 3.00 4.0
34、0 5.00 6.00 7.00 8.00 9.00 10.00 48.4 72.6 96.9 121.2 145.5 169.9 194.3 218.8 243.3 490.3 740.9 995.2 1252.9 1514.1 1778.7 2046.4 2317.1 2590.6 0.9985 0.9977 0.9969 0.9962 0.9954 0.9947 0.9939 0.9931 0.9924 0.9849 0.9776 0.9705 0.9635 0.9567 0.9502 0.9439 0.9378 0.9320 4.890 4.878 4.867 4.856 4.844
35、4.833 4.822 4.810 4.799 4.686 4.572 4.459 4.346 4.234 4.121 4.010 3.899 3.789 9.025 9.011 8.996 8.982 8.967 8.953 8.938 8.924 8.909 8.765 8.621 8.479 8.337 8.196 8.057 7.919 7.783 7.649 14.94 16.62 17.81 18.73 19.49 20.12 20.68 21.17 21.60 24.47 26.15 27.34 28.26 29.02 29.65 30.20 30.69 31.12 19.07
36、20.75 21.94 22.86 23.61 24.24 24.79 25.28 25.71 28.55 30.20 31.36 32.25 32.98 33.59 34.11 34.57 34.98 -0.0202 -0.0236 -0.0260 -0.0279 -0.0294 -0.0307 -0.0318 -0.0328 -0. O 337 -0. O 397 -0.0433 -0.0480 -0.0498 -0. O 526 -0.0538 -0.0549 -0.0459 -0.0513 Temperature = 473.15 K 0.10 25.4 0.9990 4.015 7.
37、945 11.89 15.82 -0.0166 0.20 50.9 0.9981 4.003 7.929 14.61 18.54 -0.0224 0.30 76.5 0.9971 3.991 7.913 16.21 20.13 -0.0258 0.40 102.1 0.9962 3.978 7.897 17.34 21.26 -0.0282 0.60 153.4 0.9942 3.954 7.865 18.93 22.85 -0.0317 0.70 179.1 0.9933 3.942 7.849 19.54 23.45 -0.0330 0.80 204.9 0.9923 3.930 7.83
38、3 20.07 23.97 -0.0341 0.90 230.8 0.9914 3.917 7.817 20.53 24.43 -0.0351 1.00 256.7 0.9904 3.905 7.801 20.94 24.84 -0.0360 2.00 518.2 0.9810 3.782 7.642 23.67 27.53 -0.0420 3.00 784.7 0.9718 3.658 7.481 25.26 29.09 -0.0457 4.00 1056.1 0.9627 3,534 7.321 26.40 30.18 -0.0483 6.00 1613.5 0.9453 3.282 7.
39、001 27.99 31.71 -0.0522 7.00 1899.2 0.9369 3.155 6.841 28.59 32.28 -0.0538 8.00 2189.4 0.9288 3.028 6.682 29.11 32.77 -0.0551 0.50 127.7 0.9952 3.966 7.881 18.22 22.13 -0.0301 5.00 1332.4 0.9539 3.408 7.161 27.27 31.02 -0.0504 9.00 2483.8 0.9211 2.901 6.525 29.57 33.19 -0.0564 GPA TP-L4 87 3824699 O
40、OLL4.58 b74 I 9 TABLE i. (continued) Pressure Density Z U H A G 5 MPa mol/m3 kJ/mol kJ/mol kJ/mol kJ/mol kJ/mol-K 0.10 26.9 0.20 53.8 0.30 80.8 0.40 107.9 0.50 135.0 0.60 162.2 0.70 189.5 0.80 216.8 0.90 244.2 1.00 271.6 2.00 549.8 3.00 834.7 4.00 1126.4 5.00 1425.0 6.00 1730.3 7.00 2042.5 8.00 2361
41、.2 Temperature = 448.15 K 0,9988 3.148 6.870 11.65 0.9976 3.135 6.852 14.23 0.9964 3.122 6.834 15.74 0.9952 3.108 6.817 16.82 0.9940 3.095 6.799 17.65 0.9928 3.082 6.781 18.33 0.9916 3.068 6.763 18.90 0.9904 3.055 6.746 19.40 0.9892 3.042 6.728 19.84 0.9880 3.028 6.710 20.23 0.9762 2.893 6.531 22.81
42、 0.9645 2.756 6.350 24.32 0.9530 2.616 6.167 25.39 0.9417 2.474 5.983 26.22 0.9306 2.330 5.797 26.90 0.9198 2.183 5.611 27.47 0.9093 2.035 5.423 27.97 15.37 17.95 19.46 20.52 21.35 22.03 22.60 23.09 23.52 23.91 26.45 27.92 28.94 29.73 30.37 30.90 31.35 -0.0190 -0.0248 -0.0282 -0.0306 -0.0325 -0.0340
43、 -0.0353 -0.0365 -0.0375 -0.0384 -0.0444 -0.0481 -0.0508 -0.0530 -0.0548 -0.0564 -0.0579 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1 .o0 2.00 3.00 4.00 5.00 6.00 7.00 8.00 28.5 57.0 85.7 114.4 143.2 172.1 201.1 230.1 259.3 288.5 586.0 892.7 1209.0 1535.2 1371.6 2218.3 2575.6 Temperature = 423.15
44、K 0.9985 2.301 5.814 11.35 0.9970 2.287 5.794 13.79 0.9955 2.272 5.775 15.22 0.9940 2.258 5.755 16.23 0.9925 2.243 5.735 17.02 0.9910 2.228 5.715 17.66 0.9895 2.214 5.695 18.20 0.9880 2.199 5.675 18.67 0.9865 2.184 5.655 19.08 0.9850 2.169 5.635 19.46 0.9701 2.018 5.432 21.89 0.9552 1.863 5.224 23.3
45、2 0.9404 1.703 5.012 24.33 0.9257 1.539 4.796 25.12 0.9112 1.369 4.575 25.76 0.8969 1.194 4.350 26.30 0.8829 1.015 4.121 26.76 14.87 17.30 18.72 19.73 20.51 21.14 21.68 22.15 22.56 22.92 25.31 26.68 27.64 28.37 28.96 29.45 29.87 -0.0214 -0.0272 -0.0306 -0.0330 -0.0349 -0.0365 -0.0378 -0.0389 -0.0399
46、 -0.0409 -0.0470 -0 .O507 -0.0535 -0.0557 -0.0576 -0.0593 -0.0609 GPA TP-14 87 3824699 0011459 500 10 TABLE 1. (continued) Pressure Density z U H A G 5 M Pa m0i/m3 kJ/mol kJ/mol kJ/mol kJ/mol kJ/mol-K Temperature = 398.15 K 0.10 30.3 0.9981 1.475 4.779 11.00 0.20 60.6 0.9963 1.459 4.757 13.29 0.30 9
47、1.1 0.9944 1.443 4.735 14.63 0.40 121.7 0.9925 1.426 4.712 15.59 0.50 152.5 0.9906 1.410 4.689 16.32 0.60 183.3 0.9887 1.394 4.667 16.93 0.70 214.3 0.9869 1.377 4.644 17.44 0.80 245.4 0.9850 1.360 4.621 17.88 0.90 276.6 0.9831 1.344 4.598 18.27 1.00 307.9 0.9812 1.327 4.575 18.62 2.00 627.9 0.9622 1
48、.156 4.341 20.91 3.00 961.0 0.9430 0.976 4.098 22.26 4.00 1308.2 0.9237 0.789 3.846 23.21 5.00 1670.5 0.9042 0.591 3.585 23.95 5.827P 1982.5 0.8880 0.421 3.360 24.46 14.30 16.59 17.93 18.87 19.60 20.20 20.71 21.14 21.52 21.87 24.10 25.38 26.27 26.94 27.40 -0.0239 -0.0297 -0.0331 -0.0356 -0.0375 -0.0
49、390 -O, 0403 -0.0415 -0.0425 -0.0434 -0.0496 -0.0534 -0.0563 -0.0587 -0.0604 Temperature = 373.15 K 0.10 32.3 0.9976 0.671 3.766 10.58 13.67 0.20 64.8 0.9953 0.653 3.741 12.73 15.81 0.30 97.4 0.9929 0.634 3.715 13.98 17.06 0.40 130.2 0.9905 0.616 3.689 14.88 17.95 0.50 163.1 0.9882 0.597 3.663 15.57 18.63 0.60 196.2 0.9858 0.578 3.636 16.13 19.19 0.70 229.4 0.9834 0.559 3.610 16.61 19.66 0.80 262.9 0.9810 0.540 3.584 17.03 20.07 0.90 296.4 0.9786 0.521 3.557 17.39 20.43 1.00 330.2 0.9762 0.502 3.530 17.72 20.75 2.00 677.4 0.9517 0.302 3.255 19.87 22.82 2.338P 798.
