Écoulement diphasique en milieu poreux: modèle à non-équilibre local

Abstract The assumption of local thermal non-equilibrium that leads to a one-temperature macroscopic heat equation is often called into question. This is the case, for instance, when describing the water flooding of an overheated nuclear debris bed with an important heat source term in the solid phase. Using a technique of volume averaging as described in Carbonell and Whitaker (1984), Zanotti and Carbonell (1984), Quintard and Whitaker (1993), and Quintard et al. (1996), we obtain, starting with the pore-scale equations and under some constraints, a three-equation or three-temperature macroscopic model for describing heat transfer in a porous medium subject to a two-phase flow. Effective properties can be calculated from several local closure problems which are given in the paper. These closure problems are solved in the case of simple unit cells.

[1]  Michel Quintard,et al.  Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments , 1995 .

[2]  Georges Berthoud,et al.  Development of a multidimensional model for the premixing phase of a fuel-coolant interaction , 1994 .

[3]  Kent S. Udell,et al.  Heat transfer in porous media considering phase change and capillarity—the heat pipe effect , 1985 .

[4]  Michel Quintard,et al.  Two-medium treatment of heat transfer in porous media: numerical results for effective properties , 1997 .

[5]  R. H. Nilson,et al.  Natural Convection in Porous Media with Heat Generation , 1977 .

[6]  J. Chu,et al.  The viscosity of pseudo-plastic fluids , 1954 .

[7]  T. G. Theofanous,et al.  Premixing-related behavior of steam explosions , 1995 .

[8]  R. G. Carbonell,et al.  Development of transport equations for multiphase system—I: General Development for two phase system , 1984 .

[9]  S. Whitaker,et al.  One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems , 1993 .

[10]  Michel Quintard,et al.  Diffusion in isotropic and anisotropic porous systems: Three-dimensional calculations , 1993 .

[11]  Michel Quintard,et al.  Transport in chemically and mechanically heterogeneous porous media. II: Comparison with numerical experiments for slightly compressible single-phase flow , 1996 .

[12]  Stephen Whitaker,et al.  Heat and Mass Transfer in Porous Media , 1984 .

[13]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  D. F. Fletcher,et al.  Buoyancy-driven, transient,two-dimensional thermohydrodynamics of a melt-water-steam mixture , 1988 .

[15]  S. M. Ghiaasiaan,et al.  Numerical modeling of condensing two-phase flows , 1996 .

[16]  T. G. Theofanous,et al.  Premixing of steam explosions: a three-fluid model , 1991 .

[17]  C. Moyne.  Two-equation model for a diffusive process in porous media using the volume averaging method with an unsteady-state closure , 1997 .

[18]  T. Theofanous,et al.  Triggering and propagation of steam explosions , 1991 .

[19]  Determination of permeability tensors for two-phase flow in homogeneous porous media: Theory , 1996 .

[20]  W. G. Gray,et al.  A derivation of the equations for multi-phase transport , 1975 .

[21]  Michel Quintard,et al.  Transport in chemically and mechanically heterogeneous porous media V. Two-equation model for solute transport with adsorption , 1998 .

[22]  Kenneth E. Torrance,et al.  Stability of boiling in porous media , 1990 .