Abstract
Numerical simulation of gas migration driven by compressible two-phase partially miscible flow in porous media is of major importance for safety assessment of deep geological repositories for long-lived high-level nuclear waste. We present modeling of compositional liquid and gas flow for numerical simulations of hydrogen migration in deep geological radioactive waste repository based on persistent primary variables. Two-phase flow is considered, with incompressible liquid and compressible gas, which includes capillary effects, gas dissolution, and diffusivity. After discussing briefly the existing approaches to deal with phase appearance and disappearance problem, including a persistent set of variables already considered in a previous paper (Bourgeat et al., Comput Geosci 13(1):29–42, 2009), we focus on a new variant of the primary variables: dissolved hydrogen mass concentration and liquid pressure. This choice leads to a unique and consistent formulation in liquid saturated and unsaturated regions, which is well adapted to heterogeneous media. We use this new set of variable for numerical simulations and show computational evidences of its adequacy to simulate gas phase appearance and disappearance in different but typical situations for gas migration in an underground radioactive waste repository.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abadpour A., Panfilov M.: Method of negative saturations for two-phase compositional flow with oversaturated zones. Transp. Porous Media 79, 197–214 (2009)
Allen III, M.B.: Numerical modelling of multiphase flow in porous media. Adv. Water Resour. 8, 162–187 (1985)
Andra, D.: http://www.andra.fr/international/pages/en/dossier-2005-1636.html (2005). Accessed 25 October 2012
Angelini, O., Chavant, C., Chénier, E., Eymard, R., Granet, S.: Finite volume approximation of a diffusion–dissolution model and application to nuclear waste storage. Math. Comput. Simul. 81, 2001–2017 (2011)
Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1979)
Bear, J., Bachmat, Y.: Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer, Dordrecht (1991)
Bear, J., Bensabat, J., Nir, A.: Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model. Transp. Porous Media 6, 281–298 (1991)
Bonina, B., Colina, M., Dutfoy, A.: Pressure building during the early stages of gas production in a radioactive waste repository. J. Nucl. Mater. 281(1), 1–14 (2000)
Bourgeat, A., Jurak, M., Smaï, F.: Two partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository. Comput. Geosci. 13(1), 29–42 (2009)
Brooks, R.J., Corey, A.T.: Properties of porous media affecting fluid flow. In: Proc. Am. Soc. Civil Eng. (IR2); J. Irrig. Drain. Div. 92, 61–88 (1966)
CEA: Cast3m, http://www-cast3m.cea.fr (2003). Accessed 25 January 2012
Chavent, G., Jaffré, J.: Mathematical Models and Finite Elements for Reservoir Simulation. North-Holland, Amsterdam (1986)
Class, H., Helmig, R., Bastian, P.: Numerical simulation of non-isothermal multiphase multicomponent processes in porous media 1. An efficient solution technique. Adv. Water Resour. 25, 533–550 (2002)
Class, H., Dahle, H.K., Helmig, R. (eds.): Special issue: numerical models for carbon-dioxide storage in geological formations. Comput. Geosci. 13(4), 405–509 (2009)
Delshad, M., Thomas, S.G., Wheeler, M.F.: Parallel numerical reservoir simulations of non-isothermal compositional flow and chemistry. SPE-118847-PP (2009)
Facchinei, F., Pang, J.S.: Finite Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)
Firoozabadi, A.: Thermodynamics of Hydrocarbon Reservoirs. McGraw-Hill, New York (1999)
FORGE project: http://www.forgeproject.org (2012). Accessed 25 October 2012
Draft report on definition of benchmark studies on repository-scale numerical simulations of gas migration, FORGE Reports, D1.1. http://www.bgs.ac.uk/forge/docs/reports/D1.1.pdf (2009). Accessed 25 October 2012
Progress report on benchmark studies on repository-scale numerical simulations of gas migration, FORGE Work Packages 2 Reports, D1.3. http://www.bgs.ac.uk/forge/docs/reports/D1.3.pdf (2010). Accessed 25 October 2012
Forsytha, P.A., Unger, A.J.A., Sudicky, E.A.: Nonlinear iteration methods for nonequilibrium multiphase subsurface flow. Adv. Water Resour. 21, 433–449 (1998)
Jaffré, J., Sboui, A.: Henry’s law and gas phase disappearance. Transp. Porous Media 82, 521–526 (2010)
Jin, Y., Jury, W.A.: Characterizing the dependence of gas diffusion coefficient on soil properties. Soil Sci. Soc. Am. J. 60, 66–71 (1996)
Knabner, P., Marchand, E., Müller, T.: Fully coupled generalised hybrid-mixed finite element approximation of two-phases two-components flow in porous media. Part II: numerical scheme and numerical results. Comput. Geosc. 16, 691–708 (2012)
Kräutle, S.: The semismooth Newton method for multicomponent reactive transport with minerals. Adv. Water Res. 34, 137–151 (2011)
Lauser, A., Hager, C., Helmig, R., Wohlmuth, B.: A new approach for phase transitions in miscible multi-phase flow in porous media. Adv. Water Resour. 34, 957–966 (2011)
Marle, C.M.: Multiphase Flow in Porous Media. Édition Technip, Paris (1981)
Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(3), 513–522 (1976)
NAGRA: Demonstration of disposal feasibility for spent fuel, vitrified waste and long-lived intermediate-level waste. Technical report NTB 02-05 (2002)
NDA: Geological disposal: steps towards implementation (2010)
NEA: Engineered Barrier Systems (EBS): design requirements and constraints, workshop proceedings, Turku, Finland, 26–29 August 2003. In co-operation with the European Commission and hosted by Posiva Oy, OECD/Nuclear Energy Agency, Paris, France (2004)
Oladyshkin, S., Panfilov, M.: Hydrogen penetration in water through porous medium: application to a radioactive waste storage site. Environ. Earth Sci. 64(4), 989–999 (2011). doi:10.1007/s12665-011-0916-0
Olivella, S., Alonso, E.E.: Gas flow through clay barriers. Geotechnique 58(3), 157–176 (2008)
Safety of Geological Disposal of High-level and Long-lived Radioactive Waste in France, OECD 2006, NEA No. 6178. http://www.oecd-nea.org/rwm/reports/2006/nea6178-argile.pdf. Accessed 25 October 2012
Olivella, S., Carrera, J., Gens, A., Alonso, E.E.: Non-isothermal multiphase flow of brine and gas through saline media. Transp. Porous Media 15, 271–293 (1994).
ONDRAF/NIRAS: Safir 2. Safety Assessment and Feasibility Interim Report 2, NIROND 2001-06E, Brussels, Belgium (2001)
PAMINA project: http://www.ip-pamina.eu (2011). Accessed 25 January 2012
Panday, S., Forsyth, P.A., Falta, R.W., Wu, Y.-S., Huyakorn, P.S.: Considerations for robust compositional simulations of subsurface nonaqueous phase liquid contamination and remediation. Water Resour. Res. 31, 1273–1289 (1995)
Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation. Elsevier, Amsterdam (1977)
Pruess, K., Oldenburg, C., Moridis, G.: Tough2 user’s guide, version 2.0. Lawrence Berkeley National Laboratory, Berkeley (1999)
Talandier, J.: Synthèse du benchmark couplex-gaz. In: Journées Scientifiques du GNR MoMaS, Lyon, 4–5 Septembre 2008. http://momas.univ-lyon1.fr/presentations/couplex_lyon2008_andra.ppt. Accessed 25 January 2012
Van Genuchten, M.: A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)
Wua, Y.-S., Forsyth, P.A.: On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media. J. Contam. Hydrol. 48, 277–304 (2001)
Hintermuller, M., Ito, K., Kunisch, K.: The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13, 865–888 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bourgeat, A., Jurak, M. & Smaï, F. On persistent primary variables for numerical modeling of gas migration in a nuclear waste repository. Comput Geosci 17, 287–305 (2013). https://doi.org/10.1007/s10596-012-9331-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-012-9331-1