Abstract
The main purpose of this article is to investigate, both theoretically and computationally, the effects of mineral dissolution ratios on the different respects of chemical-dissolution front instability problems in fluid-saturated porous media. In order to get a better understanding of how the mineral dissolution ratio affects the propagation and evolution of a planar chemical-dissolution front in an infinite space consisting of a fluid-saturated porous medium, the theoretical analysis method is used to derive the generous solution to the propagation speed of the planar chemical-dissolution front, while the computational simulation method is employed to simulate the detailed evolution process when the planar chemical-dissolution front is evolved into complicated morphologies at the supercritical Zhao numbers. The related theoretical results reveal that the mineral dissolution ratio plays an important role in controlling the propagation speed of a planar chemical-dissolution front in the fluid-saturated porous medium. An increase in the value of the mineral dissolution ratio can result in a remarkable decrease in the value of the propagation speed of a planar chemical-dissolution front. On the other hand, the related computational simulation results demonstrate that the mineral dissolution ratio has a considerable influence on the evolution pattern of a planar chemical-dissolution front during its propagation in the fluid-saturated porous medium. An increase in the mineral dissolution ratio can reduce the likelihood for a planar chemical-dissolution front to evolve from the initial planar shape into different morphologies within the fluid-saturated porous medium of finite size.
Similar content being viewed by others
References
Alt-Epping P., Smith L.: Computing geochemical mass transfer and water/rock ratios in submarine hydrothermal systems: implications for estimating the vigour of convection. Geofluids 1, 163–181 (2001). doi:10.1046/j.1468-8123.2001.00014.x
Bear J.: Dynamics of Fluids in Porous Media. Elsevier, Amsterdam (1972)
Chadam J., Hoff D., Merino E., Ortoleva P., Sen A.: Reactive infiltration instabilities. IMA J. Appl. Math. 36, 207–221 (1986). doi:10.1093/imamat/36.3.207
Chadam J., Ortoleva P., Sen A.: A weekly nonlinear stability analysis of the reactive infiltration interface. IMA J. Appl. Math. 48, 1362–1378 (1988)
Chen J.S., Liu C.W.: Numerical simulation of the evolution of aquifer porosity and species concentrations during reactive transport. Comput. Geosci. 28, 485–499 (2002). doi:10.1016/S0098-3004(01)00084-X
Holzbecher E.O.: Modeling Density-Driven Flow in Porous Media. Springer, Berlin (1998)
Lewis R.W., Schrefler B.A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. Wiley, New York (1998)
Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (1992)
Ormond A., Ortoleva P.: Numerical modeling of reaction-induced cavities in a porous rock. J. Geophys. Res. 105, 16737–16747 (2000). doi:10.1029/2000JB900116
Ortoleva P., Chadam J., Merino E., Sen A.: Geochemical self-organization II: the reactive-infiltration instability. Am. J. Sci. 287, 1008–1040 (1987)
Phillips O.M.: Flow and Reactions in Permeable Rocks. Cambridge University Press, Cambridge (1991)
Raffensperger J.P., Garven G.: The formation of unconformity-type uranium ore deposits: coupled hydrochemical modelling. Am. J. Sci. 295, 639–696 (1995)
Schafer D., Schafer W., Kinzelbach W.: Simulation of reactive processes related to biodegradation in aquifers: 1. Structure of the three-dimensional reactive transport model. J. Contam. Hydrol. 31, 167–186 (1998a). doi:10.1016/S0169-7722(97)00060-0
Schafer D., Schafer W., Kinzelbach W.: Simulation of reactive processes related to biodegradation in aquifers: 2. Model application to a column study on organic carbon degradation. J. Contam. Hydrol. 31, 187–209 (1998b). doi:10.1016/S0169-7722(97)00061-2
Scheidegger A.E.: General theory of dispersion in porous media. J. Geophys. Res. 66, 3273–3278 (1961). doi:10.1029/JZ066i010p03273
Scheidegger A.E.: The Physics of Flow Through Porous Media. University of Toronto Press, Toronto (1974)
Steefel C.I., Lasaga A.C.: Evolution of dissolution patterns: permeability change due to coupled flow and reaction. In: Melchior, D.C., Basset, R.L. (eds) Chemical Modeling in Aqueous Systems II. American Chemical Society Symposium Series No. 416, pp. 213–225. American Chemical Society, Washington (1990)
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, 529–592 (1994)
Xu T.F., Samper J., Ayora C., Manzano M., Custodio E.: Modelling of non-isothermal multi-component reactive transport in field scale porous media flow systems. J. Hydrol. (Amst.) 214, 144–164 (1999). doi:10.1016/S0022-1694(98)00283-2
Yeh G.T., Tripathi V.S.: A model for simulating transport of reactive multispecies components: model development and demonstration. Water Resour. Res. 27, 3075–3094 (1991). doi:10.1029/91WR02028
Zhao C., Xu T.P., Valliappan S.: Numerical modeling of mass transport problems in porous media: a review. Comput. Struc. 53, 849–860 (1994). doi:10.1016/0045-7949(94)90373-5
Zhao C., Hobbs B.E., Mühlhaus H.B.: Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses. Comput. Methods Appl. Mech. Eng. 165, 175–186 (1998). doi:10.1016/S0045-7825(98)00038-3
Zhao C., Hobbs B.E., Mühlhaus H.B., Ord A.: Finite element modelling of rock alteration and metamorphic process in hydrothermal systems. Commun. Numer. Methods Eng. 17, 833–843 (2001). doi:10.1002/cnm.455
Zhao C., Hobbs B.E., Mühlhaus H.B., Ord A., Lin G.: Finite element modeling of three-dimensional steady-state convection and lead/zinc mineralization in fluid-saturated rocks. J. Comput. Methods Sci. Eng. 3, 73–89 (2003)
Zhao C., Hobbs B.E., Ord A., Peng S., Mühlhaus H.B., Liu L.: Numerical modeling of chemical effects of magma solidification problems in porous rocks. Int. J. Numer. Methods Eng. 64, 709–728 (2005). doi:10.1002/nme.1372
Zhao C., Hobbs B.E., Hornby P., Ord A., Peng S.: Numerical modelling of fluids mixing, heat transfer and non-equilibrium redox chemical reactions in fluid-saturated porous rocks. Int. J. Numer. Methods Eng. 66, 1061–1078 (2006). doi:10.1002/nme.1581
Zhao C., Hobbs B.E., Ord A., Hornby P., Peng S.: Effect of reactive surface areas associated with different particle shapes on chemical-dissolution front instability in fluid-saturated porous rocks. Transp. Porous Media 73, 75–94 (2008a). doi:10.1007/s11242-007-9162-z
Zhao C., Hobbs B.E., Hornby P., Ord A., Peng S., Liu L.: Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. Int. J. Numer. Anal. Methods Geomech. 32, 1107–1130 (2008b). doi:10.1002/nag.661
Zhao C., Hobbs B.E., Ord A.: Fundamentals of Computational Geoscience. Springer, Berlin (2009)
Zienkiewicz O.C.: The Finite Element Method. McGraw-Hill, London (1977)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, C., Hobbs, B.E., Ord, A. et al. Effects of Mineral Dissolution Ratios on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media. Transp Porous Med 82, 317–335 (2010). https://doi.org/10.1007/s11242-009-9427-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-009-9427-9