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Looking for some reference solutions for the reactive transport benchmark of MoMaS with SPECY. (English) Zbl 1425.76235
Summary: Numerical benchmark can be an efficient way to validate reactive transport codes. The reactive transport benchmark of GNR MoMaS is here presented and solved on its easy 1D version. The reactive transport code SPECY is presented with a brief description of its main numerical methods: discontinuous finite elements for solving advection, mixed hybrid finite elements for solving dispersion and Newton-Raphson method to linearise the equilibrium chemistry and respect of the chemically allowed interval and positive continuous fractions methods to increase the robustness of the chemistry resolution. By successive mesh and time step refinement, we use the reactive transport code SPECY to look for a reference solution to this problem.

MSC:
76S05 Flows in porous media; filtration; seepage
76V05 Reaction effects in flows
76M10 Finite element methods applied to problems in fluid mechanics
76-04 Software, source code, etc. for problems pertaining to fluid mechanics
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[1] Aggarwal, M., Carrayrou, J.: Parameter estimation for reactive transport by a Monte-Carlo approach. AIChE J. 52(6), 2281–2289 (2006)
[2] Appelo, C.A.J., Verweij, E., Schafer, H.: A hydrogeochemical transport model for an oxidation experiment with pyrite/calcite/exchangers/organic matter containing sand. Appl. Geochem. 13(2), 257–268 (1998)
[3] Carrayrou J., Kern, M., Knabner, P.: Reactive transport benchmark of MoMaS. Comput. Geosci. (2009). doi: 10.1007/s10596-009-9157-7 · Zbl 1425.76236
[4] Carrayrou, J., Mosé, R., Behra, P.: New efficient algorithm for solving thermodynamic chemistry. AIChE J. 48(4), 894–904 (2002)
[5] Carrayrou, J., Mosé, R., Behra, P.: Modelling reactive transport in porous media: iterative scheme and combination of discontinuous and mixed-hybrid finite elements. C. R. Acad. Sci. Serie II: Mec. Phys. Chim. Sci. Terre Univers 331(3), 211–216 (2003) · Zbl 1255.76074
[6] Cederberg, A., Street, R.L., Leckie, J.O.: A groundwater mass transport and equilibrium chemistry model for multicomponent systems. Water Resour. Res. 21, 1095–1104 (1985)
[7] Davis, T.A., Duffs, I.S.: A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Trans. Math. Softw. 25(1), 1–20 (1999) · Zbl 0962.65027
[8] De Windt, L., Burnol, A., Montarnal, P., van der Lee, J.: Intercomparison of reactive transport models applied to UO2 oxidative dissolution and uranium migration. J. Contam. Hydrol. 61(1–4), 303–312 (2003)
[9] Fahs, M., Carrayrou, J., Younes, A., Ackerer, P.: On the efficiency of the direct substitution approach for reactive transport problems in porous media. Water Air Soil Pollut. 193(1–4), 299–308 (2008)
[10] Hammond, G.E., Valocchi, A.J., Lichtner, P.C.: Modeling multicomponent reactive transport on parallel computers using Jacobian–Free Newton Krylov with operator-split preconditioning. In: Hassanizadeh, S.M. (ed.) Developments in Water Science Computational Methods in Water Resources. Proceedings of the XIVth International Conference on Computational Methods in Water Resources (CMWR XIV), pp. 727–734. Elsevier, Amsterdam (2002)
[11] Hoffmann, J., Kräutle, S., Knabner, P.: A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem. Comput. Geosci. (2009, in press) · Zbl 1425.76240
[12] Holm, T.R.: Comment on ”Computing the equilibrium composition of aqueous systems: an iterative solution at each step in Newton–Raphson”. Environ. Sci. Technol. 23(12), 1531–1532 (1989)
[13] Konikow, L.F., Bredehoeft, J.D.: Ground-water models cannot be validated. Adv. Water Resour. 15(1), 75–83 (1992)
[14] Lagneau, V., van der Lee, J.: HYTEC results of the MoMas reactive transport benchmark. Comput. Geosci. (2009). doi: 10.1007/s10596-009-9159-5 · Zbl 1425.76247
[15] Lichtner, P.C.: Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems. Geochim. Cosmochim. Acta 49(3), 779–800 (1985)
[16] Nowack, B., Mayer, K.U., Oswald, S.E., Van Beinum, W., Appelo, C.A.J., Jacques, D., Seuntjens, P., Rard, F., Jaillard, B., Schnepf, A., Roose, T.: Verification and intercomparison of reactive transport codes to describe root-uptake. Plant Soil 285(1–2), 305–321 (2006)
[17] Oreskes, N., Shrader-Frechette, K., Belitz, K.: Verification, validation, and confirmation of numerical models in the earth sciences. Science 263(5147), 641–646 (1994)
[18] Parkhurst, D.L., Appelo, C.A.J.: User’s guide to PHREEQC (version 2)–a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. US Geological Survey, Rep 99-4259, 312 pp. (1999)
[19] Pruess, K., Garcia, J., Kovscek, T., Oldenburg, C., Rutqvist, J., Steefel, C., Xu, T.: Code intercomparison builds confidence in numerical simulation models for geologic disposal of CO2. Energy 29(9–10), 1431–1444 (2004)
[20] Siegel, P., Mosé, R., Jaffré, J.: Solution of the advection dispersion equation using a combination of discontinuous and mixed finite elements. Int. J. Numer. Methods Fluids 24, 595–613 (1997) · Zbl 0894.76041
[21] Steefel, C.I., Lasaga, A.C.: 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(5), 529–592 (1994)
[22] Steefel, C.I., MacQuarrie, K.T.B.: Approaches to modeling of reactive transport in porous media. Rev. Mineral. 34, 82–129 (1996)
[23] Steefel, C.I., DePaolo, D.J., Lichtner, P.C.: Reactive transport modeling: an essential tool and a new research approach for the Earth sciences. Earth Planet. Sci. Lett. 240(3–4), 539–558 (2005)
[24] Valocchi, A.J., Street, R.L., Roberts, P.V.: Transport of ion-exchanging solutes in groundwater: chromatographic theory and field simulation. Water Resour. Res. 17, 1517–1527 (1981)
[25] van der Lee, J., De Windt, L.: Present state and future directions of modeling of geochemistry in hydrogeological systems. J. Contam. Hydrol. 47(2–4), 265–282 (2001)
[26] van der Lee, J., De Windt, L., Lagneau, V., Goblet, P.: Module-oriented modeling of reactive transport with HYTEC. Comput. Geosci. 29(3), 265–275 (2003)
[27] Walter, A.L., Frind, E.O., Blowes, D.W., Ptacek, C.J., Molson, J.W.: Modeling of multicomponent reactive transport in groundwater. 1. Model development and evaluation. Water Resour. Res. 30(11), 3137–3148 (1994)
[28] Yeh, G.T., Tripathi, V.S.: A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components. Water Resour. Res. 25(1), 93–108 (1989)
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