A mathematical model of dissolution of rocks has been developed with regard for the specifics of the dissolution processes in the porous space of rocks. The factors determined by this specificity have been revealed. The influence of the capacitive properties of rocks changing in the course of the dissolution process has been studied. An analytical solution of the karst problem is constructed. An expression is obtained for the rate of the progress of the karsting process.
Similar content being viewed by others
References
V. Zh. Arens, Physical and Chemical Geotechnology [in Russian], Izd. Moskovs. Gos. Gorn. Univ., Moscow (2001).
A. G. Kasatkin, Basic Processes and Apparatuses of Chemical Technology [in Russian], Izd. “Al’yans,” Moscow (2004).
V. I. Petrukhin, Construction on Saline Soils [in Russian], Stroiizdat, Moscow (1989).
A. I. Perel’man, Geochemistry [in Russian], Izd. “Lenand,” Moscow (2016).
A. V. Lekhov, Physical and Chemical Hydrodynamics [in Russian], Izd. "KDU," Moscow (2010).
W. Dreybrodt, Processes in Karst Systems: Physics, Chemistry and Geology, Springer Verlag, Berlin–Heidelberg (1988).
V. V. Tolmachev and F. Roiter, Engineering Karsting [in Russian], Nedra, Moscow (1990).
G. Kaufmann and J. Braun, Karst aquifer evolution in fractured rocks, Water Resour. Res., 35, No. 1, 3223–3238 (1999).
F. Gabrovsek and W. Dreybrodt, Role of mixing corrosion in calcite-aggressive H2O–2–CaCO3 solutions in the early evolution of karst aquifers in limestone, Water Resour. Res., 36, No. 6, 1177–1188 (2000).
G. Kaufmann and J. Braun, Karst aquifer evolution in fractured, porous rocks, Water Resour. Res., 36, No. 1, 1381–1391 (2000).
R. Liedl, M. Sauter, D. Huckinghaus, T. Clemens, and G. Teutsch, Simulation of the development of karst aquifers using a coupled continuum pipe flow model, Water Resour. Res., 39, No. 3, CitelD 1057 (2003); https://doi.org/10.1029/2001WR001206.
R. B. Hanna and H. Rajaram, Influence of aperture variability on dissolutional growth of fissures in karst formations, Water Resour. Res., 34, No. 11, 2843–2853 (1998).
G. Kaufmann, Numerical models for mixing corrosion in natural and artificial karst environments, Water Resour. Res., 39, No. 6, CitelD 1157 (2003); https://doi.org/10.1029/2002WR001707.
F. Gabrovsek and W. Dreybrodt, A model of the early evolution of karst aquifers in limestone in the dimensions of length and depth, J. Hydrol., 240, 206–224 (2001).
V. N. Nikolaevskii, Geomechanics and Fluid Dynamics [in Russian], Nedra, Moscow (1996).
M. Khramchenkov and E. Khramchenkov, A new approach to obtain rheological relations for saturated porous media, Int. J. Rock Mech. Mining Sci., 72, 49–53 (2014).
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow (1987).
Sh. K. Gimatudinov and A. I. Shirkovskii, Physics of the Oil and Gas Reservoir [in Russian], Nedra, Moscow (1982).
E. S. Romm, Structural Models of the Pore Space of Rocks [in Russian], Nedra, Leningrad (1985).
V. G. Levich, Physicochemical Hydrodynamics [in Russian], Izd. AN SSSR, Moscow (1952).
A. V. Kosterin, M. G. Khramchenkov, and V. A. Chugunov, Mass transfer during filtration in a porous medium with a soluble skeleton, J. Eng. Phys. Thermophys., 60, No. 6, 720–724 (1991).
M. G. Khramchenkov, Modeling the microkinetics of heterogeneous chemical reactions during the filtration of a solution, Geokhimiya, No. 12, 1304–1309 (1998).
G. P. Brovka, I. N. Dorozhok, and S. N. Ivanov, Computational schemes for the processes of convective-diffusion transport of water-soluble compounds, J. Eng. Phys. Thermophys., 83, No. 5, 922–928 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 4, pp. 912–917, July–August, 2022.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Khramchenkov, M.G. Mathematical Simulation of Dissolution of Rocks in the Course of Karsting Processes. J Eng Phys Thermophy 95, 896–901 (2022). https://doi.org/10.1007/s10891-022-02548-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-022-02548-1