Modelling and Applications of Transport Phenomena in Porous Media

1 EIGHT LECTURES ON MATHEMATICAL MODELLING OF TRANSPORT IN POROUS MEDIA.- 1.1 Lecture One: Introduction.- 1.1.1 Porous medium.- 1.1.2 Modelling process.- 1.1.3 Selecting the size of an REV.- 1.2 Lecture Two: Microscopic Balance Equations.- 1.2.1 Velocity and flux.- 1.2.2 The general balance equation.- 1.2.3 Particular balance equations.- 1.2.4 Averaging rules.- 1.3 Lecture Three: Macroscopic Balance Equations.- 1.3.1 General balance equation.- 1.3.2 Particular cases.- 1.3.3 Stress in porous media.- 1.4 Lecture Four: Advective Flux.- 1.4.1 Advective flux of a single fluid that occupies the entire void space.- 1.4.2 Particular cases.- 1.4.3 Multiphase flow.- 1.5 Lecture Five: Complete Transport Model.- 1.5.1 Boundary conditions.- 1.5.2 Content of a complete model.- 1.6 Lecture Six: Modelling Mass Transport of a Single Fluid Phase Under Isothermal Conditions.- 1.6.1 Basic mass balance equations.- 1.6.2 Stationary nondeformable solid skeleton.- 1.6.3 Deformable porous medium.- 1.6.4 Boundary conditions.- 1.6.5 Complete mathematical model.- 1.7 Lecture Seven: Diffusive Flux.- 1.7.1 Diffusive mass flux.- 1.7.2 Diffusive heat flux.- 1.8 Lecture Eight: Modelling Contaminant Transport.- 1.8.1 The Phenomenon of dispersion.- 1.8.2 Fluxes.- 1.8.3 Sources and Sinks.- 1.8.4 Mass balance equation for a single component.- 1.8.5 Balance equations with immobile liquid.- 1.8.6 Balance equations for radionuclide decay chain.- 1.8.7 Two multicomponent phases.- 1.8.8 Boundary Conditions.- 1.8.9 Complete Mathematical Model.- References.- List of Main Symbols.- 2 MULTIPHASE FLOW IN POROUS MEDIA Th. DRACOS Swiss Federal Inst. of Technology (E.T.H.) Zurich, Switzerland.- 2.1 Capillary Pressure.- 2.1.1 Interfacial tension, contact angle and wettability.- 2.1.2 Interfacial curvature and capillary pressure.- 2.1.3 Equilibrium between a liquid and its vapor.- 2.1.4 Microscopic domain.- 2.1.5 Macroscopic space.- 2.1.6 Phase distribution in the pore space.- 2.2 Flow Equations for Immiscible Fluids.- 2.3 Mass Balance Equations.- 2.4 Simultaneous Flow of Two Fluids having a Small Density Difference.- 2.5 Measurement of the relations pc?i(S?i), and kr,?i(S?i).- 2.6 Mathematical descripton of the relations between pc,wSwand k,r,w.- 2.7 Complete Statement of Multiphase Flow Problems.- 2.8 Solute transport in multiphase flow through porous media.- References.- List of Main Symbols.- 3 PHASE CHANGE PHENOMENA AT LIQUID SATURATED SELF HEATED PARTICULATE BEDS J-M. BUCHLIN and A. STUBOS von Karman Institute for Fluid Dynamics Rhode Saint Genese B-1640, Belgium.- 3.1 Introduction.- 3.2 Preboiling Phenomenology.- 3.3 Boiling regime and dryout heat flux.- 3.4 Constitutive Relationships-Bed Disturbances.- 3.4.1 Introduction.- 3.4.2 Bed permeability.- 3.4.3 Relative permeabilities and passabilities.- 3.4.4 Capillary pressure.- 3.4.5 Bed structural changes.- 3.5 Conclusions.- A. Zero-Dimensional Model.- B. Fractional downward heat flux by conduction.- C. Sub cooled zone thickness at the top of the bed.- References.- List of Main Symbols.- 4 HEAT TRANSFER IN SELF-HEATED PARTICLE BEDS SUBMERGED IN LIQUID COOLANT KENT MEHR and JORGEN WURTZ Commission of the European Communities Joint Research Centre, Ispra, Italy.- 4.1 The PAHR Scenario.- 4.2 Specific PAHR Phenomena.- 4.2.1 Bed characteristics.- 4.2.2 Heat conduction.- 4.2.3 Boiling debris beds.- 4.2.4 Dryout.- 4.2.5 Downward boiling.- 4.2.6 Unsteady state.- 4.2.7 Channeling.- 4.3 PAHR-2D.- 4.3.1 Basic equations.- 4.3.2 Spatial discretisation.- 4.3.3 Boundary conditions.- 4.3.4 Time integration.- 4.3.5 Solution procedure.- 4.3.6 D10 Post test calculation.- 4.3.7 Steep power ramp.- 4.4 In-pile experiments.- 4.4.1 Boiling.- 4.4.2 Dryout.- 4.4.3 Bed disturbance.- References.- List of Main Symbols.- 5 PHYSICAL MECHANISMS DURING THE DRYING OF A POROUS MEDIUM CH. MOYNE, CH. BASILICO, J. CH. BATSALE and A._DEGIOVANNI. Laboratoire d'Energetique et de Mecanique Theorique et Appliquee U.A. C.N.R.S. 875, Ecoles des Mines, Nancy, France.- 5.1 General Aspects of the Drying Process.- 5.1.1 The three drying periods.- 5.1.2 The characteristic drying curve concept.- 5.1.3 Conclusion.- 5.2 A General Model for Simultaneous Heat and Mass Transfer in a Porous Medium.- 5.2.1 The fundamental hypotheses of the model.- 5.2.2 Phenomenological laws.- 5.2.3 Conservation laws.- 5.2.4 System to be solved.- 5.2.5 Numerical solution.- 5.3 Application to Drying.- 5.3.1 High temperature convective drying.- 5.3.2 Low temperature convective drying.- 5.3.3 The diffusion model.- 5.3.4 Receding drying front.- 5.4 Conclusions.- References.- List of Main Symbols.- 6 STOCHASTIC DESCRIPTION OF POROUS MEDIA G. DE MARSILY Ecole des Mines de Paris, l'Universite Pierre et Marie Curie Paris, France.- 6.1 Definition of Properties of Porous Media: The Example of Porosity.- 6.2 Stochastic Approach to Permeability and Spatial Variability.- 6.3 Stochastic Partial Differential Equations.- 6.3.1 Properties of stochastic partial differential equations.- 6.3.2 Spectral methods.- 6.3.3 The method of perturbations.- 6.3.4 Simulation method (Monte-Carlo).- 6.4 Example of stochastic solution to the transport equation.- 6.5 The problem of estimation of a RF by kriging.- 6.6 The intrinsic hypothesis: definition of the variogram.- 6.6.1 The intrinsic hypothesis.- 6.6.2 Determination of the variogram.- 6.6.3 Behaviour of the variogram for large h.- 6.6.4 Behaviour close to the origin.- 6.6.5 Anisotropy in the variogram.- 6.7 Conclusions.- References.- List of Main Symbols.