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Gas Migration in Highly Water-Saturated Opalinus Clay Microfractures Using a Two-Phase TRT LBM

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Abstract

Hydrogen gas migration modeling through water-saturated engineering barriers and the host rock of a deep geological repository for radioactive waste is of concern for safety assessment of such facilities. A two-phase two-relaxation-time lattice Boltzmann model using the Rothman and Keller approach was parallelized on graphic processing units to simulate hydrogen gas migration in a 3D image obtained by X-ray microtomography of Opalinus clay microfractures. A dimensional analysis combined with a grid refinement analysis was carried out to set the model parameters to reproduce the realistic viscous, capillary and inertial forces of the natural system. Relative permeabilities curves were first calculated in a simple regular fracture with different initial two-phase configurations. We observed that segmented gas flow configurations led to a drop in the relative gas permeability by two orders of magnitude as compared to parallel flow configuration. The model was then applied to 4\(\times \) refined 3D images. For lower water saturation values (\(0.5 \le S_\mathrm{w} < 0.7\)), hydrogen gas migrated through continuous gas paths oriented in the flow direction. At high water saturation values (\(S_\mathrm{w}\ge 0.7\)), the relative gas permeability dropped to zero because the hydrogen phase segmented into gas pockets that were stuck in local narrow throats of the clay fracture. The study pointed out that the high capillary forces prevented the gas bubbles from distorting themselves to pass through these narrow paths.

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References

  • Banari, A., Janßsen, C., Grilli, S.T., Krafczyk, M.: Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios. Comput. Fluids 93, 1–17 (2014)

    Article  Google Scholar 

  • Blunt, M.J., Bijlijk, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)

    Article  Google Scholar 

  • Blumling, P., Bernier, F., Lebon, P., Martin, C.D.: The excavation damaged zone in clay formations time-dependent behaviour and influence on performance assessment. Phys. Chem. Earth 32, 588–599 (2007)

    Article  Google Scholar 

  • Boulini, P.F., Angulo-Jaramillo, R., Daian, J.-F., Talandier, J., Berne, P.: Pore gas connectivity analysis in Callovo-Oxfordian argillite. Appl. Clay Sci. 42(1–2), 276–283 (2008)

    Article  Google Scholar 

  • Boulini, P.F., Angulo-Jaramillo, R., Talandier, J., Berne, P., Daian, J.-F.: Contribution of the Dusty Gas Model to permeability/diffusion tests on partially saturated clay rocks. Transp. Porous Media 93, 609–634 (2012)

    Article  Google Scholar 

  • Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)

    Article  Google Scholar 

  • Cariou, S., Skozylas, F., Dormieux, L.: Experimental measurements and water transfer models for the drying of argillite. Int. J. Rock Mech. Min. Sci. 54, 56–69 (2012)

    Google Scholar 

  • Croisé, J., Mayer, G., Talandier, J., Wendling, J.: Impact of water consumption and saturation-dependent corrosion rate on hydrogen generation and migration from an intermediate-level radioactive waste repository. Transp. Porous Media 90(1), 59–75 (2011)

    Article  Google Scholar 

  • Cottin, C., Bodiguel, H., Colin, A.: Drainage in two-dimensional porous media: from capillary fingering to viscous flow. Phys. Rev. E 82, 046315 (2010)

    Article  Google Scholar 

  • Dawson, G., Lee, S., Juet, A.: The trapping and release of bubbles from a linear pore. J. Fluid Mech. 722, 437–460 (2013)

    Article  Google Scholar 

  • Delay, J., Vinsot, A., Krieguer, J.M., Rebours, H., Armand, G.: Making of the underground scientific experimental programme at the Meuse/Haute-Marne underground research laboratory. Phys. Chem. Earth 32, 2–18 (2007)

    Article  Google Scholar 

  • Didier, M.: Etude du transfert réactif de l’hydrogène au sein de l’argilite intacte. Ph.D. thesis, Université de Grenoble (2012)

  • Dou, Z., Zhou, Z.-F.: Numerical study of non-uniqueness of the factors influencing relative permeability in heterogeneous porous media by lattice Boltzmann method. Int. J. Heat Fluid Flow 42, 23–32 (2013)

    Article  Google Scholar 

  • Dymitrowska, L.M., Pazdniakou, A., Adler, P.M.: Two-phase-flow pore-size simulations in Opalinus clay by the lattice Boltzmann method. In: Norris, S., Bruno, J., Cathelineau, M., Delage, P., Fairhurst, C., Gaucher, E.C., Höhn, E.H., Kalinichev, A., Lalieux, P., Sellin, P. (eds.) Clays in Natural and Engineered Barriers for Radioactive Waste Confinement, vol. 400, pp. 195–206. Geological Society, Special Publications, London (2014)

    Google Scholar 

  • El Mendili, Y., Abdelouas, A., Bardeau, J.-F.: Insight into the mechanism of carbon steel corrosion under aerobic and anaerobic conditions. Phys. Chem. Chem. Phys. 15, 9197–9204 (2013)

    Article  Google Scholar 

  • Frisch, U., d’Humières, D., Hasslacher, B., Lallemand, P., Pomeau, Y., Rivert, J.-P.: Lattice gas hydrodynamics in two and three dimensions. Complex Syst. 1, 649–707 (1987)

    Google Scholar 

  • Genty, A.: Validation expérimentale d’un modèle numérique de déplacement diphasique en milieu poreux. Ph.D. thesis, Ecole Nationale Supérieure des Mines de Paris (1996)

  • Ginzbourg, I., Adler, P.M.: Boundary flow condition analysis for three-dimensional lattice Boltzmann model. J. Phys. II France 4, 191–214 (1994)

    Article  Google Scholar 

  • Ginzburg, I., d’Humières, D.: Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 68, 066614 (2003)

    Article  Google Scholar 

  • Ginzburg, I.: Lattice Boltzmann modeling with discontinuous collision components: hydrodynamic and advection-diffusion equations. J. Stat. Phys. (2006). doi:10.1007/s10955-006-9234-4

    Google Scholar 

  • Giraud, A., Giot, R., Homand, F., Koriche, A.: Permeability identification of a weakly permeable partially saturated porous media. Transp. Porous Media 69(2), 259–280 (2007)

    Article  Google Scholar 

  • Gustensen, A.K., Rothman, D.H., Zaleski, S., Anetti, G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43, 4320–4327 (1991)

    Article  Google Scholar 

  • Homsy, G.M.: Viscous fingering in porous media. Ann. Rev. Fluid Mech. 19, 271–311 (1987)

    Article  Google Scholar 

  • Huang, H., Huang, J.-J., Lu, X.-Y.: Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method. Comput. Fluids 93, 164–172 (2014)

    Article  Google Scholar 

  • Huang, H., Thorne, D.T., Schaap, M.G., Sukop, M.C.: Proposed approximation for contact angles in Shan-and-Chen-type muticomponent multiphase lattice Boltzmann models. Phys. Rev. E 76, 066701 (2007)

    Article  Google Scholar 

  • Huang, H., Lu, X.-Y.: Relative permeabilities and coupling effects in steady-state gas-liquid phase in porous media: a lattice Boltzmann study. Phys. fluids 21, 092104 (2009)

    Article  Google Scholar 

  • Huang, H., Sukop, M., Lu, X.: Multiphase Latice Boltzmann Methods: Theory and Application. Wiley-Blackwell, New York (2015). ISBN 978-1-118-97133-8

    Book  Google Scholar 

  • d’Humières, D., Lallemand, P.: Lattice gas automata for fluid mechanics. Phys. A: Stat. Mech. Its Appl. 140(1–2), 326–335 (1986)

    Article  Google Scholar 

  • d’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L.-S.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos. Trans. R. Soc. A 360, 437–451 (2002)

    Article  Google Scholar 

  • d’Humières, D., Ginzburg, I.: Viscosity independent numerical errors for lattice Boltzmann models: from recurrence equations to “magic” collision numbers. Comput. Math. Appl. 58(5), 823–840 (2009)

    Article  Google Scholar 

  • Jougnot, D., Revil, A., Lu, N., Wayllace, A.: Transport properties of the Callovo-Oxfordian clay rock under partially saturated conditions. Water Resour. Res. 46, 08514 (2010)

    Article  Google Scholar 

  • Khirevich, S., Ginzburg, I., Tallarek, U.: Coarse- and fine-grid numerical beahvior of MRT/TRT lattice-Boltzmann schemes in regular and random sphere packings. J. Comput. Phys. 281, 708–742 (2014)

    Article  Google Scholar 

  • Kuznik, F., Obrecht, C., Rusaouen, G., Roux, J.-J.: LBM based flow simulation using GPU computing processor. Comput. Math. Appl. 59(7), 2380–2392 (2009)

    Article  Google Scholar 

  • Lallemand, P., Luo, L.-S.: Theory of the lattice Boltzmann method: dispersion, isotropy, Galilean invariance and stability. Phys. Rev. E 61, 6546 (2000)

    Article  Google Scholar 

  • Lammers P., Küster U.: Recent performance results of the lattice boltzmann method. In: Resch M., Bönisch T., Tiyyagura S., Furui T., Seo Y., Bez W. (eds.) High Performance Computing on Vector Systems 2006, pp. 51–59. Springer (2007)

  • Latva-Kokko, M., Rothman, D.H.: Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys. Rev. E 71, 056702 (2005)

    Article  Google Scholar 

  • Latva-Kokko, M., Rothman, D.H.: Static contact angle in lattice Boltzmann models of immiscible fluids. Phys. Rev. E 72, 046701 (2005)

    Article  Google Scholar 

  • Leclaire, S., Reggio, M., Trépanier, J.-Y.: Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model. Comput. Fluids 48, 98–112 (2011)

    Article  Google Scholar 

  • Leclaire, S., Reggio, M., Trépanier, J.-Y.: Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model. Appl. Math. Model. 36, 2237–2252 (2012)

    Article  Google Scholar 

  • Leclaire, S., Pellerin, N., Reggio, M., Trépanier, J.-Y.: Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models. Int. J. Multiph. Flow 57, 159–168 (2013)

    Article  Google Scholar 

  • Lenormand, R., Touboul, E., Zarcone, C.: Numerical models and experiments on immiscible displacements in porous media. J. Fluid. Mech. 189, 165–187 (1988)

    Article  Google Scholar 

  • Lenormand, R., Zarcone, C.: Capillary fingering: percolation and fractal dimension. Transp. Porous Media 4, 599–612 (1989)

    Article  Google Scholar 

  • Liu, H., Valocchi, A.J., Kang, Q.: Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations. Phys. Rev. E 85, 046309 (2012)

    Article  Google Scholar 

  • Liu, H., Valocchi, A.J., Werth, C., Kang, Q., Oostrom, M.: Pore-scale simulation of liquid CO\(_{2}\) displacement of water using a two-phase lattice Boltzmann model. Adv. Water Resour. 73, 144–158 (2014)

    Article  Google Scholar 

  • Liu, H., Kang, Q., Leonardi, C.R., Schmieschek, S., Narvaez, A., Jones, B.D., Williams, J.R., Valocchi, A.J., Harting, J.: Multiphase lattice Boltzmann simulations for porous media applications. A review. Comput. Geosci. (2015). doi:10.1007/s10596-015-9542-3

    Google Scholar 

  • Lishchuk, S.V., Care, C.M., Halliday, I.: Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents. Phys. Rev. E 67, 036701 (2003)

    Article  Google Scholar 

  • Marschall, P., Horseman, S., Gimmi, T.: Characterization of gas transport properties of the Opalinus Clay, a potential host rock formation for radioactive waste disposal. Oil Gas Sci. Technol. 60, 121–139 (2005)

    Article  Google Scholar 

  • Matray, J.M., Parneix, J.C., Tinseau, E., Prt, D., Mayor, J.C.: Structural organization of porosity in the Opalinus Clay at the Mont Terri Rock Laboratory under saturated and unsaturated conditions. Clays in Natural & engineered barriers for radioactive waste confinement, International meeting, Lille, France (2007)

    Google Scholar 

  • Raeini, A.Q., Blunt, M.J., Bijeljic, B.: Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces. Adv. Water Resour. 74, 116–126 (2014)

    Article  Google Scholar 

  • Rinaldi, P.R., Dalponte, D.G., Venere, M.J., Clausse, A.: Cellular automata algorithm for simulation of surface flows in large plains. Simul. Model. Pract. Theory 15(3), 315–327 (2007)

    Article  Google Scholar 

  • Rinaldi, P.R., Dari, E.A., Venere, M.J., Clausse, A.: A lattice-Boltzmann solver for 3D fluid simulation on GPU. Simul. Model. Pract. Theory 25, 163–171 (2012)

    Article  Google Scholar 

  • Sarrot, V., Prat, M.: Hyperslow drainage in a porous medium. Influence of retention curve. Adv. Water Resour. 33, 987–996 (2014)

    Article  Google Scholar 

  • Senger, R., Ewing, J., Zhang, K., Avis, J., Marschall, P., Gaus, I.: Modeling approaches for investigating gas migration from a deep low/intermediate level waste repository (Switzerland). Transp. Porous Media 90(1), 113–133 (2011)

    Article  Google Scholar 

  • Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47(3), 1815–1820 (1993)

    Article  Google Scholar 

  • Sukop, M.C., Huang, H., Lin, C.L., Deo, D., Oh, K., Miller, J.D.: Distribution of multiphase fluids in porous media: comparison between lattice Boltzmann modeling and micro X-ray tomography. Phys. Rev. E 77, 026710 (2008)

    Article  Google Scholar 

  • Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E 54, 5041–5052 (1996)

    Article  Google Scholar 

  • Talon, L., Bauer, D., Gland, N., Youssef, S., Auradou, H., Ginzburg, I.: Assessment of the two relaxation time lattice-Boltzmann scheme to simulate Stokes flow in porous media. Water Resour. Res. 48, W04526 (2012). doi:10.1029/2011WR0113859

    Article  Google Scholar 

  • Tolke, J.: Implementation of a lattice Boltzmann kernel using the compute unified device architecture developed by nVIDIA. Comput. Vis. Sci. 13(1), 29–39 (2010)

    Article  Google Scholar 

  • Tsakiroglou, C.D., Theodoropoulou, M.A., Karoutsos, V., Papanicolaou, D.: Determination of the effective transport coefficients of pore networks from transient immiscible and miscible displacement experiments. Water Resour. Res. 41, 29–39 (2005)

    Article  Google Scholar 

  • Vardon, P.J., Thomas, H.R., Masum, A.S., Chen, Q., Nicholson, D.: Simulation of repository gas migration in a bentonite buffer. Eng. Comput. Mech. 167(EM 1), 13–22 (2014)

  • Xu, B., Yortos, Y., Salin, D.: Invasion percolation with viscous forces. Phys. Rev. E 57, 739–751 (1998)

    Article  Google Scholar 

  • Xu, T., Senger, R., Finsterle, S.: Corrosion-induced gas generation in a nuclear waste repository: reactive geochemistry and multiphase flow effects. Appl. Geochem. 23(12), 3423–3433 (2008)

    Article  Google Scholar 

  • Yang, D.: Caractérisation par la mesure de perméabilité au gaz de l’endommagement mécanique et hydrique dans l’EDZ des argilites du Callovo-Oxfordien. Ph.D. thesis, École Supérieure Nationale des Mines de Paris (2008)

  • Yang, D., Billotte, J., Su, K.: Characterization of the hydromechanical behavior of argillaceous rocks with effective gas permeability under deviatoric stress. Eng. Geol. 114(3 V4), 116–122 (2010)

  • Yang, J., Boek, E.S.: A comparison study of multi-component lattice Boltzmann models for flow in porous media applications. Comput. Math. Appl. 65(6), 882–890 (2013)

    Article  Google Scholar 

  • Zhao, Y.: Lattice Boltzmann based on PDE Solver on the GPU. Vis. Comput. 24(5), 29–39 (2007)

    Google Scholar 

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Acknowledgements

The authors acknowledge the financial support of the NEEDS-MIPOR program within “Mission for Interdisciplinarity” of the French National Centre for Scientific Research. The authors would also like to acknowledge the help of Aliaksei Pazdniakou for his useful remarks.

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Correspondence to Seifallah Ben Hadj Hassine.

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Hassine, S.B.H., Dymitrowska, M., Pot, V. et al. Gas Migration in Highly Water-Saturated Opalinus Clay Microfractures Using a Two-Phase TRT LBM. Transp Porous Med 116, 975–1003 (2017). https://doi.org/10.1007/s11242-016-0809-5

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