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Environmental Earth Sciences

, Volume 62, Issue 6, pp 1197–1207 | Cite as

Non-isothermal flow in low permeable porous media: a comparison of Richards’ and two-phase flow approaches

  • Wenqing Wang
  • Jonny Rutqvist
  • Uwe-Jens Görke
  • Jens T. Birkholzer
  • Olaf Kolditz
Original Article

Abstract

The present work compares the performance of two alternative flow models for the simulation of thermal-hydraulic coupled processes in low permeable porous media: non-isothermal Richards’ and two-phase flow concepts. Both models take vaporization processes into account: however, the Richards’ model neglects dynamic pressure variations and bulk flow of the gaseous phase. For the comparison of the two approaches first published, data from a laboratory experiment are studied involving thermally driven moisture flow in a partially saturated bentonite sample. Then a benchmark test of longer-term thermal-hydraulic behavior in the engineered barrier system of a geological nuclear waste repository is analyzed (DECOVALEX project). It was found that both models can be used to reproduce the vaporization process if the intrinsic permeability is relative high. However, when a thermal-hydraulic coupled problem has the same low intrinsic permeability, only the two-phase flow approach provides reasonable results.

Keywords

Non-isothermal two-phase flow Richards’ approximation Porous media CTF1 experiment DECOVALEX task D 

Notes

Acknowledgments

The development of the numerical models was conducted in the framework of the international DECOVALEX project. The funding from the Federal Institute for Geosciences is highly acknowledged (Dr. Shao). This work is part of the PoF research initiative of the Helmholtz Association within the Environmental Engineering and Geothermal Technology programs. Funding from the Swedish Radiation Safety Authority (SSM) through the US Department of Energy Contract No. DE-AC02-05CH11231 is greatly appreciated.

References

  1. Alkan H, Müller W (2008) Approaches for modelling gas flow in clay formations as repository systems. Phys Chem Earth 33(Suppl 1):S260–S268Google Scholar
  2. Alonso EE, Alcoverro J, Coste F et al (2005) The FEBEX benchmark test: case definition and comparison of modelling approaches. Int J Rock Mech Min Sci 42:611–638CrossRefGoogle Scholar
  3. Barr D, Birkholzer JT, Rutqvist J, Sonnenthal E (2004) Draft description for DECOVALEX-THMC Task D: long-term permeability/porosity changes in EDZ and near field, due to THM and THC processes in volcanic and crystalline-bentonite systems. Technical report, Earth Sciences Division, Lawrence Berkeley National Laboratory, USAGoogle Scholar
  4. Börgesson L (1985) Water flow and swelling pressure in non-saturated bentonite-based clay barriers. Eng Geol 21:229–237CrossRefGoogle Scholar
  5. Börgesson L, Chijimatsu M, Fujita T, Nguyen TS, Rutqvist J, Jing L (2001) Thermo-hydro-mechanical characterization of a bentonite-based buffer material by laboratory tests and numerical back analyses. Int J Rock Mech Min Sci 38:95–104CrossRefGoogle Scholar
  6. Bruel D (2002) Impact of induced thermal stresses during circulation tests in an engineered fractured geothermal reservoir: example of the Soultzsous-Forets European hot fractured rock geothermal project, RhineGraben, France. Geothermics 57:459–470Google Scholar
  7. Chijimatsu M, Börgesson L, Fujita T, Jussila P, Nguyen TS, Rutqvist J, Jing L (2009) Model development and calibration for the coupled thermal, hydraulic and mechanical phenomena of the bentonite. Environ Geol 57:1255–1261CrossRefGoogle Scholar
  8. Freiboth S, Class H, Helmig R, Graf T, Ehlers W, Schwarz V, Vrettos Ch (2009) A model for multiphase flow and transport in porous media including a phenomenological approach to account for deformation-a model concept and its validation within a code intercomparison study. Comput Geosci 13:281-300CrossRefGoogle Scholar
  9. Gens A, Alonso EE (1992) Framework for the behaviour of unsaturated expansive clays. Can Geotech J 29:1013–1032CrossRefGoogle Scholar
  10. Gou R, Dixon D (2006) Thermohydromechanical simulations of the natural cooling stage of the Tunnel Sealing Experiment. Eng Geol 85:313–331CrossRefGoogle Scholar
  11. Gray WG, Hassanizadeh SM (1991) Unsaturated flow theory including interfacial phenomena. Water Resour Res 27:1855–1963CrossRefGoogle Scholar
  12. Jang WY, Aral MM (2009) Multiphase flow fields in in-situ air sparging and its effect on remediation. Transp Porous Media 76:99–119CrossRefGoogle Scholar
  13. Kohl T, Evans KF, Hopkirk RJ, Rybach L (1995) Coupled hydraulic, thermal and mechanical considerations for the simulation of hot dry rock reservoirs. Geothermics 24:345–359CrossRefGoogle Scholar
  14. Kolditz O, Diersch H-J (1993) Quasi steady-state strategy for numerical simulation of geothermal circulation processes in hot dry rock fracture. Int J Non Linear Mech 28:467–481CrossRefGoogle Scholar
  15. Kolditz O, De Jonge JD (2004) Non-isothermal two-phase flow in low-permeable porous media. Comput Mech 33:345–364CrossRefGoogle Scholar
  16. Kuhn M, Bartels J, Iffland J (2002) Predicting reservoir property trends under heat exploitation: interaction between flow, heat transfer, transport, and chemical reactions in a deep aquifer at Stralsund, Germany. Geothermics 31:725–749CrossRefGoogle Scholar
  17. Lewis RW, Schrefler BA (1998) The finite element method in the static and dynamic deformation and consolidation of porous media, 2nd edn. Wiley, ChichesterGoogle Scholar
  18. Li Q, Wu Z, Bai Y, Yin X, Li X (2006) Thermo-hydro-mechanical modeling of CO2 sequestration system around fault environment. Pure Appl Geophys 163:2585–2593CrossRefGoogle Scholar
  19. Nguyen TS, Börgesson L, Chijimatsu M, Hernelind J, Jing L, Kobayashi A, Rutqvist J (2009) A case study on the influence of THM coupling on the near field safety of a spent fuel repository in sparsely fractured granite. Environ Geol 57:1239–1254CrossRefGoogle Scholar
  20. Olivella S, Gens A (2000) Vapour transport in low permeability unsaturated soils with capillary effects. Transp Porous Media 40:219–241CrossRefGoogle Scholar
  21. O’Sullivan MJ, Pruess K, Lippmann MJ (2001) State of the art of geothermal reservoir simulation. Geothermics 30:395–429CrossRefGoogle Scholar
  22. Philip JR, de Vries DA (1957) Moisture movement in porous materials under temperature gradient. Trans Am Geophys Union 38:222–232Google Scholar
  23. Pruess K (2008) On CO2 fluid flow and heat transfer behavior in the subsurface, following leakage from a geologic storage reservoir. Environ Geol 54:1677–1686CrossRefGoogle Scholar
  24. Rutqvist J, Börgesson L, Chijimatsu M, Kobayashi A, Nguyen TS, Jing L, Noorishad J, Tsang CF (2001) Thermohydromechanics of partially saturated geological media—governing equations and formulation of four finite element models. Int J Rock Mech Min Sci 38:105–127CrossRefGoogle Scholar
  25. Rutqvist J, Wu Y-S, Tsang C-F, Bodvarsson G (2002) A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. Int J Rock Mech Min Sci 39:429-442CrossRefGoogle Scholar
  26. Rutqvist J, Barr D, Birkholzer JT, Chijimatsu M, Kolditz O, Liu Q, Oda Y, Wang W, Zhang C (2008) Results from an international simulation study on coupled thermal, hydrological, and mechanical processes near geological nuclear waste repositories. Nucl Technol 163:101–109Google Scholar
  27. Rutqvist J, Barr D, Birkholzer JT, Fujisaki K, Kolditz O, Liu Q, Fujita T, Wang W, Zhang C (2009) A comparative simulation study of coupled THM processes and their effect on fractured rock permeability around nuclear waste repositories. Environ Geol 57:1347–1360CrossRefGoogle Scholar
  28. Sanavia L, Pesavento F, Schrefler BA (2006) Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation. Comput Mech 37:331–348CrossRefGoogle Scholar
  29. Schrefler BA, Matteazzi R, Gawin D, Wang X (2000) Two parallel computing methods for coupled thermohydromechanical problems. Comput Aided Civ Infrastruct Eng 15:176–188CrossRefGoogle Scholar
  30. Tsang C (1991) Coupled hydromechanical-thermochemical processes in rock fractures. Rev Geophys 29:537–551CrossRefGoogle Scholar
  31. van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898CrossRefGoogle Scholar
  32. Villar MV, Fernandez AM, Cuevas J (1997) Caracterización Geoquímica de bentonita compactada: efectos producidos por flujo termohidráulico. Interim Report FEBEX, Informe 70-IMA-M-0-2, CIEMAT, MadridGoogle Scholar
  33. Wang W, Kosakowski G, Kolditz O (2009) A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media. Comput Geosci 35:1631–1641CrossRefGoogle Scholar
  34. Zhang XY, Zhu YM, Fang CH (2009) The role for air flow in soil slope stability analysis. J Hydrodyn 21:640–646CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Wenqing Wang
    • 1
  • Jonny Rutqvist
    • 2
  • Uwe-Jens Görke
    • 1
  • Jens T. Birkholzer
    • 2
  • Olaf Kolditz
    • 1
  1. 1.Helmholtz Centre for Environmental Research, UFZLeipzigGermany
  2. 2.Lawrence Berkeley National LaboratoryBerkeleyUSA

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