Abstract
The formulation of self-similar problems of single- and two-phase water and vapor flow through high-permeability rocks is considered in the case when heat conduction is unimportant. The properties of the corresponding system of conservation laws, which affect the relative position of the integral curves of the Riemann waves and the discontinuity adiabatic curves, are investigated. The problem of breakdown of an arbitrary discontinuity in a geothermal formation with supercritical water parameters is solved.
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References
G.I. Barenblatt, V.M. Entov, and V.M. Ryzhik, Motion of Liquids and Gases in Natural Formations (Nedra, Moscow, 1984) [in Russian].
A.A. Barmin and G.G. Tsypkin, “Mathematical Model of Water Injection into a Geothermal Steam-Saturated Reservoir,” Fluid Dynamics 31(6), 874–879 (1996).
A.A. Barmin and A.V. Kondrashov, “Two-Front Mathematical Model of Water Injection into a Steam-Saturated Geothermal Reservoir,” Fluid Dynamics 35(3), 399–405 (2000).
A.G. Kulikovskii, “Evaporation and Condensation Fronts in Porous Media,” Fluid Dynamics 37(5), 740–746 (2002).
W. Lambert, D. Marcheshin, and J. Bruining, “On the Riemann Solutions of the Balance Equations for Steam and Water Flow in a Porous Medium,” Meth. and Appl. Anal. 12(3), 325–348 (2005).
J. Stopa and P. Wojnarowski, “Analytical Model of Cold Water Front Movement in a Geothermal Reservoir,” Geothermics 35(1), 59–69 (2006).
A.A. Afanas’ev and A.A. Barmin, “Unsteady One-Dimensional Water and Steam Flows through a Porous Medium with Allowance for Phase Transitions,” Fluid Dynamics 42(4), 627–636 (2007).
A.A. Afanas’ev, “Interaction of Evaporation Fronts with a Formation Interface in a Porous Medium,” Fluid Dynamics 43(3), 94–103 (2008).
M. Jackson and M. Blunt, “Elliptic Regions and Stable Solutions for Three-Phase Flow in Porous Media,” Transport Porous Media 48, 249–269 (2002).
S. Oladyshkin, J. Royer, and M. Panfilov, “Effective Solution through the Streamline Technique and HT-Splitting for the 3D Dynamic Analysis of the Compositional Flows in Oil Reservoirs,” Transport Porous Media 74, 311–329 (2008).
A.G. Kulikovskii and E.I. Sveshnikova, Nonlinear Waves in Elastic Media (Moskovskii Litsei, Moscow, 1998) [in Russian].
A.G. Kulikovskii and A.P. Chugainova, Classical and Non-Classical Discontinuities and Their Structures in Nonlinearly Elastic Media with Dispersion and Dissipation (Mathematical Institute of the Russian Academy of Sciences, Moscow, 2007), Is. 7 [in Russian].
L.D. Landau and E.M. Lifshits, Theoretical Physics, Vol. 4: Statistical Physics (Gostekhizdat, Moscow, 1951) [in Russian].
A.I. Brusilovskii, Phase Transitions during the Development of Oil and Gas Fields (Graal, Moscow, 2002) [in Russian].
A.A. Afanasyev, “Steady-State Water and Vapor Flows in a Porous Medium,” Fluid Dynamics 44(4), 545–554 (2009).
A.A. Aleksandrov and B.A. Grigoryev, Tables of the Thermophysical Characteristics of Water and Water Vapor (Publishing House of the Moscow Power Engineering Institute, Moscow, 2003) [in Russian].
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Original Russian Text © A.A. Afanasyev, 2010, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2010, Vol. 45, No. 2, pp. 72–83.
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Afanasyev, A.A. On the formulation of problems of nonisothermal water and vapor flow through a high-permeability formation. Fluid Dyn 45, 230–240 (2010). https://doi.org/10.1134/S0015462810020080
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DOI: https://doi.org/10.1134/S0015462810020080