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In the case of a two-phase medium – such as the soil, which consists of an elastic skeleton and is filled with pore fluids – stress and strain within the medium are dependent on both phases. Similarly, in the case of heat transfer, heat is conducted through the two phases at different rates, with an additional heat transfer between the phases. In the classical approach to modelling a porous medium, it is assumed that the fluid filling the pore space is water, which is incompressible. In the case of gas, the volume of which is strongly dependent on temperature and pressure, one should take this behavior into account in the constitutive relations for the medium. This work defines the physical relations of a two-phase medium and provides heat transfer equations, constructed for a porous, elastic skeleton with fluid-filled pores, which may be: liquid, gas, or mixture of liquid and a gas in non-isothermal conditions. The paper will present constitutive relations derived from the laws of irreversible thermodynamics, assuming that pores are filled with either a liquid or a gas. These relations, in the opinion of the authors, may be used as the basis for the construction of a model of the medium filled partly with a liquid and partly with a gas. It includes the possibility of independent heat transfer through any given two-phase medium phase, with the transfer of heat between the phases.
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Tom
Strony
67--78
Opis fizyczny
Bibliogr. 24 poz., rys.
Twórcy
autor
- Wrocław University of Science and Technology, Faculty of Civil Engineering, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
autor
- Wrocław University of Science and Technology, Faculty of Technology and Life Sciences, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
- [1] AURIAULT J.L., Dynamic Behaviour of a Porous Medium Saturated by a Newtonian Fluid, Int. J. Engng. Sc., 1980, Vol. 18.
- [2] AURIAULT J.L., STRZELECKI T., BAUER J., HE S., Porous deformable Media Saturated by a Very Compressible Fluid, Eur. J. Mech. A/Solid, 1990, Vol. 9, 4.
- [3] AURIAULT J.L., Heterogeneous Medium. Is an Equivalent Macroscopic Description Possible?, Int. J. Engng. Sci., 1991, 29, 7.
- [4] BENSOUSSAN A., LIONS J.L., PAPANICOLAU G., Asymptotic Analysis for Periodic Structures, Amsterdam: Holland Publishing Company, 1978.
- [5] BIOT M.A., Le probleme de la Consolidation des Matieres Argileuses sous une charge, B. 55 Ann. Soc. Sci., 1935, Bruxelles 110/113.
- [6] BIOT M.A., General Theory of three-dimensional Consolidation, J. Appl. Physics, 1941, Vol. 12.
- [7] BIOT M.A., Theory of Stress-Strain Relation in Anisotropic Viscoelasticity and relaxation Phenomena, J. Appl. Phys., 1954, 25.
- [8] BIOT M.A., WILLIS D.G., The Elastic Coefficients of the Theory of Consolidation, J. Appl. Mech., 1957, 24.
- [9] BARTLEWSKA M., STRZELECKI T., Equations of Biot’s consolidation with Kelvin–Voight rheological frame, Studia Geotechnica et Mechanica, 2009, 31(2).
- [10] COUSSY O., Revisiting the constitutive equations of unsaturated porous solids using a Lagrangian saturation concept, Int. J. Numer. Anal. Meth. Geomech. 2007, 31.
- [11] COUSSY O., Mechanics and Physics of Porous Solids, John Wiley, 2010.
- [12] DERSKI W., Outline of continuum mechanics, PWN, Warszawa 1975, (in Polish).
- [13] DE GROOT S.R., MAZUR P., Non-equilibrium Thermodynamics, Amsterdam: North-Holland Publishing Company, 1984.
- [14] FlexPDE 6 (PDE Solutions, 2015); www.pdesolutions.com
- [15] KISIEL I., An outline of soil rheology, effect of static loading on soil, Arkady, Warszawa 1966, (in Polish).
- [16] KISIEL I., DERSKI W., IZBICKI R., MRÓZ Z., Rock and soil mechanics, PWN, Warszawa 1982, (in Polish).
- [17] ŁYDŻBA D., Constitutive equations of gas-coal medium, Studia Geotechnica et Mechanica, 1991, 13(3-4).
- [18] ŁYDŻBA D., Applications of asymptotic homogenisation method in soil and rock mechanics,: Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2002, (in Polish).
- [19] NOWACKI W., Theory of elasticity, PWN, Warszawa 1970, (in Polish).
- [20] STRZELECKI T., BAUER J., AURIAULT J.L., Constitutive equation of a gas-filled two-phase medium, Transport in Porous Media, 1993, 10.
- [21] STRZELECKI T., AURIAULT J.L., BAUER J., KOSTECKI S., PUŁA W., Mechanics of heterogeneous media. Homogenization theory, Lower Silesia Educational Publishers, Wrocław 1998, (in Polish).
- [22] STRZELECKI T., KOSTECKI S., ŻAK S., Modeling of flows through porous media, Lower Silesia Educational Publishers, Wrocław 2008, (in Polish).
- [23] STRZELECKI T., STRZELECKI M., Relation between filtration and soil consolidation theories, Studia Geotechnica et Mechanica, 2015, 37(1), 105-114.
- [24] UCIECHOWSKA A., STRZELECKI T., The influence of the type of pore fluid in two phase media on the form of consolidation equations, [in:] M. Kwaśniewski & D. Łydżba (eds.), Rock Mechanics for Resources, London: Taylor & Francis Group, Energy and Environment, 2013, 491-495.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-eaf39f72-e67c-476d-9d1e-60625632eebc