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Volumn 41, Issue 6, 2007, Pages 975-1000

Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model

Author keywords

Diffusion; Dissolution; Finite volume method; Kinetics; Precipitation

Indexed keywords


EID: 37449013673     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2007047     Document Type: Article
Times cited : (24)

References (32)
  • 1
    • 0019897571 scopus 로고
    • Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions, I, Theorical considerations
    • P. Aagaard and H.C. Helgeson, Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions, I, Theorical considerations. Am. J. Sci. 282 (1982) 237-285.
    • (1982) Am. J. Sci , vol.282 , pp. 237-285
    • Aagaard, P.1    Helgeson, H.C.2
  • 2
    • 30944457719 scopus 로고    scopus 로고
    • Assessment of diffusive and mechanical properties of hardened cement pastes using a multi-coated sphere assemblage model
    • B. Bary and S. Béjaoui, Assessment of diffusive and mechanical properties of hardened cement pastes using a multi-coated sphere assemblage model. Gem. Conor. Res. 36 (2006) 245-258.
    • (2006) Gem. Conor. Res , vol.36 , pp. 245-258
    • Bary, B.1    Béjaoui, S.2
  • 3
    • 0142087796 scopus 로고    scopus 로고
    • A reaction diffusion system with fast reversible reaction
    • D. Bothe and D. Hilhorst, A reaction diffusion system with fast reversible reaction. J. Math. Anal. Appl. 286 (2003) 125-135.
    • (2003) J. Math. Anal. Appl , vol.286 , pp. 125-135
    • Bothe, D.1    Hilhorst, D.2
  • 4
    • 37449034839 scopus 로고    scopus 로고
    • N. Bouillard, P. Montarnal and R. Herbin, Development of numerical methods for the reactive transport of chemical species in a porous media: a nonlinear conjugate gradient method, in Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering, Coupled Problems (2005), M. Papadrakis, E. Onate and B. Schroffer Eds., CIMNE, Barcelona, Spain, p. 229, ISBN: 84-95999-71-4, available on CD. See also: http://hal.archives-ouvert8B.fr/ .
    • N. Bouillard, P. Montarnal and R. Herbin, Development of numerical methods for the reactive transport of chemical species in a porous media: a nonlinear conjugate gradient method, in Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering, Coupled Problems (2005), M. Papadrakis, E. Onate and B. Schroffer Eds., CIMNE, Barcelona, Spain, p. 229, ISBN: 84-95999-71-4, available on CD. See also: http://hal.archives-ouvert8B.fr/ .
  • 6
    • 0012915707 scopus 로고    scopus 로고
    • An error estimate for a finite volume scheme forba nonlinear hyperbolic equation on a triangular mesh
    • R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, An error estimate for a finite volume scheme forba nonlinear hyperbolic equation on a triangular mesh. IMA J. Numer. Anal. 18 (1998) 563-594.
    • (1998) IMA J. Numer. Anal , vol.18 , pp. 563-594
    • Eymard, R.1    Gallouët, T.2    Ghilani, M.3    Herbin, R.4
  • 7
    • 0039526846 scopus 로고    scopus 로고
    • Convergence of finite volume schemes for semilinear convection diffusion equations
    • R. Eymard, T. Gallouët and R. Herbin, Convergence of finite volume schemes for semilinear convection diffusion equations. Numer. Math. 82 (1999) 91-116.
    • (1999) Numer. Math , vol.82 , pp. 91-116
    • Eymard, R.1    Gallouët, T.2    Herbin, R.3
  • 9
    • 70350322945 scopus 로고    scopus 로고
    • R. Eymard, T. Gallouët and R. Herbin, Finite Methods, in Techniques of Scientific Computing (Part III), Handbook for Numerical Analysis VII, P.G Ciarlet and J.L. Lions Eds., North Holland (2000) 713-1020.
    • R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, in Techniques of Scientific Computing (Part III), Handbook for Numerical Analysis VII, P.G Ciarlet and J.L. Lions Eds., North Holland (2000) 713-1020.
  • 10
    • 0035730553 scopus 로고    scopus 로고
    • Approximation by the finite volume method of an ellipticparabolic equation arising in environmental studies
    • R. Eymard, T. Gallouët, M. Gutnic, R. Herbin and D. Hilhorst, Approximation by the finite volume method of an ellipticparabolic equation arising in environmental studies. Math. Models Methods Appl. Sci. 11 (2001) 1505-1528.
    • (2001) Math. Models Methods Appl. Sci , vol.11 , pp. 1505-1528
    • Eymard, R.1    Gallouët, T.2    Gutnic, M.3    Herbin, R.4    Hilhorst, D.5
  • 12
    • 0036022623 scopus 로고    scopus 로고
    • Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
    • R. Eymard, T. Gallouët, R. Herbin and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations. Num. Math. 92 (2002) 41-82.
    • (2002) Num. Math , vol.92 , pp. 41-82
    • Eymard, R.1    Gallouët, T.2    Herbin, R.3    Michel, A.4
  • 13
    • 17444389253 scopus 로고    scopus 로고
    • Quartz precipitation kinetics at 180 °C in NaCl solutions. Implications for the usability of the principle of detailed balancing
    • J. Ganor, T.J. Huston and L.M. Walter, Quartz precipitation kinetics at 180 °C in NaCl solutions. Implications for the usability of the principle of detailed balancing. Geochim. Cosmochim. Acta 69 (2005) 2043-2056.
    • (2005) Geochim. Cosmochim. Acta , vol.69 , pp. 2043-2056
    • Ganor, J.1    Huston, T.J.2    Walter, L.M.3
  • 14
    • 0036266701 scopus 로고    scopus 로고
    • Effect of fluid-sediment reaction on hydrothermal fluxes of major elements, Eastern flank of the Juan de Fuca Ridge
    • E.R. Giambalvo, C.I. Steefel, A.T. Fisher, N.D. Rosenberg and C.G. Wheat, Effect of fluid-sediment reaction on hydrothermal fluxes of major elements, Eastern flank of the Juan de Fuca Ridge. Geochim. Cosmochim. Acta 66 10 (2002) 1739-1757.
    • (2002) Geochim. Cosmochim. Acta , vol.66 , Issue.10 , pp. 1739-1757
    • Giambalvo, E.R.1    Steefel, C.I.2    Fisher, A.T.3    Rosenberg, N.D.4    Wheat, C.G.5
  • 15
    • 0030584908 scopus 로고    scopus 로고
    • The fast reaction limit for a reaction-diffusion system
    • D. Hilhorst, R. van der Hout and L. Peletier, The fast reaction limit for a reaction-diffusion system. J. Math. Anal. Appl. 199 (1996) 349-373.
    • (1996) J. Math. Anal. Appl , vol.199 , pp. 349-373
    • Hilhorst, D.1    van der Hout, R.2    Peletier, L.3
  • 16
    • 0034531152 scopus 로고    scopus 로고
    • A mathematical and numerical model for reactive fluid flow systems
    • A. Holstad, A mathematical and numerical model for reactive fluid flow systems. Comp. Geosc. 4 (2000) 103-139.
    • (2000) Comp. Geosc , vol.4 , pp. 103-139
    • Holstad, A.1
  • 17
    • 0040650239 scopus 로고
    • Reactive transport through an array of cells with semipermeable membranes
    • U. Hornung, W. Jäger and A. Mikelić, Reactive transport through an array of cells with semipermeable membranes. RAIRO Model. Math. Anal. Numer. 28 (1994) 59-94.
    • (1994) RAIRO Model. Math. Anal. Numer , vol.28 , pp. 59-94
    • Hornung, U.1    Jäger, W.2    Mikelić, A.3
  • 18
    • 0029413160 scopus 로고
    • An analysis of crystal dissolution fronts in flows through porous media. Part 1: Compatible boundary conditions
    • P. Knabner, C.J. van Duijn and S. Hengst, An analysis of crystal dissolution fronts in flows through porous media. Part 1: Compatible boundary conditions. Adv. Water Res. 18 (1995) 171-185.
    • (1995) Adv. Water Res , vol.18 , pp. 171-185
    • Knabner, P.1    van Duijn, C.J.2    Hengst, S.3
  • 19
    • 37449028570 scopus 로고    scopus 로고
    • D. Langmuir, Aqueous environmental geochemistry. Prentice Hall (1997).
    • D. Langmuir, Aqueous environmental geochemistry. Prentice Hall (1997).
  • 21
    • 0031231547 scopus 로고    scopus 로고
    • Diffusion and dissolution/precipitation in an open porous reactive medium
    • E. Maisse and J. Pousin, Diffusion and dissolution/precipitation in an open porous reactive medium. J. Comp. Appl. Math. 82 (1997) 279-290.
    • (1997) J. Comp. Appl. Math , vol.82 , pp. 279-290
    • Maisse, E.1    Pousin, J.2
  • 22
    • 4544229656 scopus 로고    scopus 로고
    • Finite element approximation of mass transfer in a porous medium with non equilibrium phase change
    • E. Maisse and J. Pousin, Finite element approximation of mass transfer in a porous medium with non equilibrium phase change. Numer. Math 12 (2004) 207-231.
    • (2004) Numer. Math , vol.12 , pp. 207-231
    • Maisse, E.1    Pousin, J.2
  • 23
    • 37449000703 scopus 로고
    • Diffusion and dissolution in a reactive porous medium: Modeling and numerical simulations
    • A.P. Bourgeat, C. Carasso, S. Luckhaus and A. Mikelic Eds, World Scientific, ISBN: 981-02-2483-4
    • E. Maisse, P. Moszkowicz and J. Pousin, Diffusion and dissolution in a reactive porous medium: modeling and numerical simulations, in Proceedings of the Mathematical modelling of flow through porous media: proceedings of the conference, A.P. Bourgeat, C. Carasso, S. Luckhaus and A. Mikelic Eds., World Scientific (1995), p. 515, ISBN: 981-02-2483-4.
    • (1995) Proceedings of the Mathematical modelling of flow through porous media: Proceedings of the conference , pp. 515
    • Maisse, E.1    Moszkowicz, P.2    Pousin, J.3
  • 24
    • 37449026969 scopus 로고    scopus 로고
    • P. Montarnal, A. Dimier, E. Deville, E. Adam, J. Gaombalet, A. Bengaouer, L. Loth and C. Chavant, Coupling methodology within the software platform Alliances, in Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering, Coupled Problems 2005, M. Papadrakis, E. Onate and B. Schreffer Eds., CIMNE, Barcelona, Spain, p. 229, ISBN: 84-95999-71-4, available on CD. See also: http://hal.archives-ouvertes.fr/.
    • P. Montarnal, A. Dimier, E. Deville, E. Adam, J. Gaombalet, A. Bengaouer, L. Loth and C. Chavant, Coupling methodology within the software platform Alliances, in Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering, Coupled Problems 2005, M. Papadrakis, E. Onate and B. Schreffer Eds., CIMNE, Barcelona, Spain, p. 229, ISBN: 84-95999-71-4, available on CD. See also: http://hal.archives-ouvertes.fr/.
  • 25
    • 0036067297 scopus 로고    scopus 로고
    • The dissolution kinetics of major sedimentary carbonate minerals
    • J.W. Morse and R.S. Arvidson, The dissolution kinetics of major sedimentary carbonate minerals. Earth Science Reviews 58 (2002) 51-84.
    • (2002) Earth Science Reviews , vol.58 , pp. 51-84
    • Morse, J.W.1    Arvidson, R.S.2
  • 26
    • 0029656930 scopus 로고    scopus 로고
    • Diffusion and dissolution in a reactive porous medium: Mathematical modelling and numerical simulations
    • P. Moszkowicz, J. Pousin and F. Sanchez, Diffusion and dissolution in a reactive porous medium: Mathematical modelling and numerical simulations. J. Comp. Appl. Math. 66 (1996) 377-389.
    • (1996) J. Comp. Appl. Math , vol.66 , pp. 377-389
    • Moszkowicz, P.1    Pousin, J.2    Sanchez, F.3
  • 27
    • 37449003059 scopus 로고    scopus 로고
    • Reactive transport modelling in the Alliances software platform
    • 13-17 June , Chapel Hill, USA
    • C. Mügler, P. Montarnal, A. Dimier and L. Trotignon, Reactive transport modelling in the Alliances software platform, in Proceeding of CMWR, 13-17 June (2004), Chapel Hill, USA (2004) 1103-1115.
    • (2004) Proceeding of CMWR , pp. 1103-1115
    • Mügler, C.1    Montarnal, P.2    Dimier, A.3    Trotignon, L.4
  • 28
    • 28844498527 scopus 로고    scopus 로고
    • Long-term performance of cement paste during combined calcium leaching-sulfate attack: Kinetics and size effect
    • D. Planel, J. Sercombe, P. Le Bescop, F. Adenot and J.-M. Torrenti, Long-term performance of cement paste during combined calcium leaching-sulfate attack: kinetics and size effect. Cem. Concr. Res. 36 (2006) 137-143.
    • (2006) Cem. Concr. Res , vol.36 , pp. 137-143
    • Planel, D.1    Sercombe, J.2    Le Bescop, P.3    Adenot, F.4    Torrenti, J.-M.5
  • 29
    • 0039923238 scopus 로고    scopus 로고
    • Infinitely fast kinetics for dissolution and diffusion in open reactive systems
    • J. Pousin, Infinitely fast kinetics for dissolution and diffusion in open reactive systems. Nonlin. Anal. 39 (2000) 261-279.
    • (2000) Nonlin. Anal , vol.39 , pp. 261-279
    • Pousin, J.1
  • 30
    • 0000195746 scopus 로고
    • Le problème de Dirichlet pour les équations elliptiques du second ordre àcoefficients discontinus
    • G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre àcoefficients discontinus. Ann. Inst. Fourier 15 (1965) 189-258.
    • (1965) Ann. Inst. Fourier , vol.15 , pp. 189-258
    • Stampacchia, G.1
  • 31
    • 0028554365 scopus 로고
    • A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems
    • C.I. Steefel and A.C. Lasaga, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. Am. J. Sci. 294 (1994) 529-592.
    • (1994) Am. J. Sci , vol.294 , pp. 529-592
    • Steefel, C.I.1    Lasaga, A.C.2
  • 32
    • 11144346796 scopus 로고    scopus 로고
    • Crystal dissolution and precipitation in porous media: Pore scale analysis
    • C.J. van Duijn and I.S. Pop, Crystal dissolution and precipitation in porous media: pore scale analysis. J. Reine Angew. Math. 577 (2004) 171-211.
    • (2004) J. Reine Angew. Math , vol.577 , pp. 171-211
    • van Duijn, C.J.1    Pop, I.S.2


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