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Evaluation of thermal equations of state for CO2 in numerical simulations

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Abstract

Three commonly used thermal equations of state for carbon dioxide, as well as the ideal gas law, have been compared against a large number of measurement data taken from the literature. Complex equations of state reach a higher accuracy than simple ones. The inaccuracy of the density function can cause large errors in fluid property correlations, such as heat capacity or viscosity. The influence of this inaccuracy on the results of numerical simulations have been evaluated by two examples: The first one assumes isothermal gas expansion from a volume, while the second one considers heat transport along a fracture. For both examples, different equations of state have been utilized. The simulations have been performed on the scientific software platform OpenGeoSys. The difference among the particular simulation results is significant. Apparently small errors in the density function can cause considerably different results of otherwise identical simulation setups.

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References

  • Bear J (1972) Dynamics of fluids in porous media. American Elevier, New York

    Google Scholar 

  • Böttcher N (2012) Thermo-hydro-mechanical-chemical processes in porous media, chap. In: Heat transport. Lecture notes in computational science and engineering. Springer, Berlin. doi:10.1007/978-3-642-27177-9

  • Böttcher N, Singh AK, Kolditz O, Liedl R (2011) Non-isothermal, compressible gas flow for the simulation of an enhanced gas recovery application. J Comput Appl Math. doi:10.1016/jcam.2011.11.013

  • Brent R (1971) An algorithm with guaranteed convergence for finding a zero of a function. Comput J 14:422–425

    Article  Google Scholar 

  • Carslaw HS, Jaeger JC (1986) Conduction of heat in soilds. Oxford science publications, Clarendon Press

  • Clifford AA, Kestin J, Wakeham WA (1979) Thermal conductivity of N2, CH4 and CO2 at room temperature and at pressures up to 35 MPa. Phys A 97:287–295

    Article  Google Scholar 

  • Cohen E, Taylor B (1986) The 1986 adjustment of the fundamental physical constants. Rev Mod Phys 59(4):1121–1148

    Article  Google Scholar 

  • Dethlefsen F, Haase C, Ebert M, Dahmke A (2011) Uncertainties of geochemical modeling during CO2 sequestration applying batch equilibrium calculations. Environ Earth Sci, pp. 1105–1117. doi:10.1007/s12665-011-1360-x

  • Duan Z, Møller N, Weare JH (1992) An equation of state for the CH4 − CO2 − H2O system: I. Pure systems from 0 to 1000°C and 0 to 8000 bar. Geochimica et Cosmochimica Acta 56:2606–2617

    Google Scholar 

  • Duschek W, Kleinrahm R, Wagner W (1990a) Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide. I. The homogeneous gas and liquid region in the temperature range from 217 K to 340 K at pressures up to 9 MPa. J Chem Thermodyn 22:827–840

    Article  Google Scholar 

  • Duschek W, Kleinrahm R, Wagner W (1990b) Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide. II. Saturated-liquid and saturated-vapour densities and the vapour pressure along the entire coexistence curve. J Chem Thermodyn 22:841–864

    Article  Google Scholar 

  • Ely JF, Haynes WM, Bain BC (1989) Isochoric (p, V m , T) measurements on CO2 and on (0.982 CO2 + 0.018N2) from 250 to 330 K at pressures to 35 MPa). J Chem Thermodyn 21:979–984

    Article  Google Scholar 

  • Fenghour A, Wakeham W, Vesovic V (1998) The viscosity of carbon dioxide. J Phys Chem Ref Data 27:31–44

    Article  Google Scholar 

  • Fenghour A, Wakeham WA, Watson JTR (1995) Amount of substance density of CO2 at temperatures from 329 K to 698 K and pressures up to 34 MPa. J Chem Thermodyn 27:219–223

    Article  Google Scholar 

  • Gilgen R, Kleinrahm R, Wagner W (1992) Measurement of the (pressure, density, temperature) relation of sulfurhexafluoride in the homogeneous region from 321.15 K to 333.15 K and on the coexistence curve from 288.15 K to 315.15 K. J Chem Thermodyn 24:953–964

    Article  Google Scholar 

  • Guildner LA (1958) The thermal conductivity of carbon dioxide in the region of the critical point. Proc Natl Acad Sci USA 44(11):1149–1153

    Article  Google Scholar 

  • Kestin J, Korfali Ö, Sengers JV (1980) Density expansion of the viscosity of carbon dioxide near the critical temperature. Phys A 100:335–348

    Article  Google Scholar 

  • Kolditz O, Bauer S, Beyer C, Böttcher N, Dietrich P, Görke UJ, Kalbacher T, Park CH, Sauer U, Schütze C, Shao H, Singh A, Taron J, Wang W, Watanabe N (2012a) A systematic benchmarking approach for geologic CO2 injection and storage. Environ Earth Sci. doi:10.1007/s12665-012-1656-5

  • Kolditz O, Bauer S, Bilke L, Böttcher N, Delfs JO, Fischer T, Görke UJ, Kalbacher T, Kosakowski G, McDermott CI, Park CH, Radu F, Rink K, Shao H, Shao HB, Sun F, Sun YY, Singh AK, Taron J, Walther M, Wang W, Watanabe N, Wu Y, Xie M, Xu, W, Zehner B (2012b) OpenGeoSys: an open source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environ Earth Sci. doi:10.1007/s12665-012-1546-x

  • Kolditz O, Görke UJ, Shao H, Wang W (2012c) Thermo-hydro-mechanical–processes in fractured porous media. In: Lecture notes in computational science and engineering, vol. 86. Springer, Berlin. doi:10.1007/978-3-642-27177-9

  • Kühn M, Görke UJ, Birkholzer J, Kolditz O (2012) CLEAN thematic issue editorial. Environ Earth Sci. doi:10.1007/s12665-012-1714-z

  • Michels A, Sengers JV, van der Gulik PS (1957) The viscosity of carbon dioxide between 0 °C and 75 °C and at pressures up to 2000 atmospheres. Physica XXIII:95–102

    Article  Google Scholar 

  • Michels A, Sengers JV, van der Gulik PS (1962) The thermal conductivity of carbon dioxide in the critical region. Physica 28:1216–1237

    Article  Google Scholar 

  • Millat J, Mustafa M, Ross M, Wakeham WA, Zalaf M (1987) Thermal conductivity of argon, carbon dioxide and nitrous oxide. Phys A 145:461–497

    Article  Google Scholar 

  • Ogata A, Banks RB (1961) A solution of the differential equation of longitudinal dispersion in porous media. Tech rep, Geological Survey (US), Washington, DC

  • Padua A, Wakeham WA, Wilhelm J (1994) The viscosity of liquid carbon dioxide. Int J Thermophys 5:767–777

    Google Scholar 

  • Park CH, Böttcher N, Wang W, Kolditz O (2011a) Are upwind techniques in multi-phase flow models necessary? J Comput Phys 230(22):8304–8312

    Article  Google Scholar 

  • Park CH, Taron J, Görke UJ, Singh A, Kolditz O (2011b) The fluidal interface is where the action is in CO2 sequestration and storage: Hydromechanical analysis of mechanical failure. Energy Procedia 4:3691–3698

    Article  Google Scholar 

  • Peng D, Robinson D (1976) A new two-constant equation of state. Ind Eng Chem Fundam 15:59–64

    Article  Google Scholar 

  • Pitzer K (1939) Corresponding states for perfect liquids. J Chem Phys 7(8):583–590

    Article  Google Scholar 

  • Scalabrin G, Marchi P, Finezzo F, Span R (2006) A reference multiparameter thermal conductivity equation for carbon dioxide with an optimized functional Form. J Phys Chem Ref Data 35(4):1549–1575

    Article  Google Scholar 

  • Scott A, Johns AI, Watson JTR (1983) Thermal conductivity of carbon dioxide in the temperature range 300–348 K and pressures up to 25 MPa. J Chem Soc Faraday Trans 1(79):733–740

    Google Scholar 

  • Singh AK, Baumann G, Hennings J, Görke UJ, Kolditz O (2012a) Numerical analysis of thermal effects during carbon dioxide injection with enhanced gas recovery: a theoretical case study for the Altmark gas field. Environ Earth Sci. doi:10.1007/s12665-012-1689-9

  • Singh AK, Pilz P, Zimmer M, Kalbacher T, Görke UJ, Kolditz O (2012b) Numerical simulation of tracer transport in the Altmark gas field. Environ Earth Sci. doi:10.1007/s12665-012-1688-x

  • Singh AK, Görke UJ, Kolditz O (2011) Numerical simulation of non-isothermal compositional gas flow: application to carbon dioxide injection into gas reservoirs. Energy 36(5):3446–3458

    Article  Google Scholar 

  • Span R, Wagner W (1996) A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J Phys Chem Ref Data 25(6):1509–1596

    Article  Google Scholar 

  • Stephan K, Krauss R, Laesecke A (1987) Viscosity and thermal conductivity of nitrogen for a wide range of fluid states. J Phys Chem Ref Data 16(4):993–1023

    Google Scholar 

  • van der Gulik PS (1997) Viscosity of carbon dioxide in the liquid phase. Phys A 238:81–112

    Article  Google Scholar 

  • Vesovic V, Wakeham W (1990) The transport properties of carbon dioxide. J Phys Chem Ref Data 19(3):763–807

    Article  Google Scholar 

  • Wang W, Rutqvist J, Görke U, Birkholzer J, Kolditz O (2011) Non-isothermal flow in low permeable porous media: a comparison of richards and two-phase flow approaches. Environ Earth Sci 62:1197–1207

    Article  Google Scholar 

  • Watanabe N, Wang W, McDermott C, Taniguchi T, Kolditz O (2010) Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media. Comput Mech 45(4):263–280

    Article  Google Scholar 

  • Weber JA (1992) Measurements of the virial coefficients and equation of state of the carbon dioxide + ethane system in the supercritical region. Int J Thermophys 13:1011–1032

    Article  Google Scholar 

  • Younglove BA, Ely JF (1987) Thermophysical properties of fluids. ii. Methane, ethane, propane, isobutane, and normal butane. J Phys Chem Ref Data 16(4):577–798

    Google Scholar 

Download references

Acknowledgments

This work was performed within the framework of the CLEAN joint research project as part of the geoscientific R&D program GEOTECHNOLOGIEN, funded by the German Federal Ministry of Education and Research (BMBF), GDF SUEZ and by basic research program at KIGAM. We like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. Technische Universität Dresden, 01062, Dresden, Germany

    Norbert Böttcher, Olaf Kolditz & Rudolf Liedl

  2. Helmholtz-Centre for Environmental Research-UFZ, Permoserstr. 15, 04318, Leipzig, Germany

    Joshua Taron & Olaf Kolditz

  3. Korea Institute of Geoscience and Mineral Resources, 124 Gwahang-no, Yuseong-gu, Daejeon, 305-350, Korea

    Chan-Hee Park

Authors
  1. Norbert Böttcher
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  2. Joshua Taron
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  3. Olaf Kolditz
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  4. Chan-Hee Park
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  5. Rudolf Liedl
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Correspondence to Norbert Böttcher.

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Böttcher, N., Taron, J., Kolditz, O. et al. Evaluation of thermal equations of state for CO2 in numerical simulations. Environ Earth Sci 67, 481–495 (2012). https://doi.org/10.1007/s12665-012-1704-1

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