Modelling and Applications of Transport Phenomena in Porous Media

Transport phenomenain porous media are encounteredin various disciplines, e. g. , civil engineering, chemical engineering, reservoir engineering, agricul tural engineering and soil science. In these disciplines, problems are en countered in which various extensive quantities, e. g. , mass and heat, are transported through a porous material domain. Often, the void space of the porous material contains two or three fluid phases, and the various ex tensive quantities are transported simultaneously through the multiphase system. In all these disciplines, decisions related to a system's development and its operation have to be made. To do so a tool is needed that will pro vide a forecast of the system's response to the implementation of proposed decisions. This response is expressed in the form of spatial and temporal distributions of the state variables that describe the system's behavior. Ex amples of such state variables are pressure, stress, strain, density, velocity, solute concentration, temperature, etc. , for each phase in the system, The tool that enables the required predictions is the model. A model may be defined as a simplified version of the real porous medium system and the transport phenomena that occur in it. Because the model is a sim plified version of the real system, no unique model exists for a given porous medium system. Different sets of simplifying assumptions, each suitable for a particular task, will result in different models.

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1 EIGHT LECTURES ON MATHEMATICAL MODELLING OF TRANSPORT IN POROUS MEDIA.- 1.1 Lecture One: Introduction.- 1.2 Lecture Two: Microscopic Balance Equations.- 1.3 Lecture Three: Macroscopic Balance Equations.- 1.4 Lecture Four: Advective Flux.- 1.5 Lecture Five: Complete Transport Model.- 1.6 Lecture Six: Modelling Mass Transport of a Single Fluid Phase Under Isothermal Conditions.- 1.8 Lecture Eight: Modelling Contaminant Transport.- 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.- 2.2 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 Genèse B-1640, Belgium.- 3.1 Introduction.- 3.2 Preboiling Phenomenology.- 3.3 Boiling regime and dryout heat flux.- 3.4 Constitutive Relationships-Bed Disturbances.- 3.5 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 WÜRTZ Commission of the European Communities Joint Research Centre, Ispra, Italy.- 4.1 The PAHR Scenario.- 4.2 Specific PAHR Phenomena.- 4.3 PAHR-2D.- 4.4 In-pileexperiments.- 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'Energétique et de Mécanique Théorique et Appliquée U.A. C.N.R.S. 875, Ecoles des Mines, Nancy, France.- 5.1 General Aspects of the Drying Process.- 5.2 A General Model for Simultaneous Heat and Mass Transfer in a Porous Medium.- 5.3 Application to Drying.- 5.4 Conclusions.- References.- List of Main Symbols.- 6 STOCHASTIC DESCRIPTION OF POROUS MEDIA G. DE MARSILY Ecole des Mines de Paris, l'Université 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.- 6.4 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.- 6.7 Conclusions.- References.- List of Main Symbols.