Recent Advances in Problems of Flow and Transport in Porous Media

Porous media, and especially phenomena of transport in such materials, are an impor1ant field of interest for geologists, hydrogeologists, researchers in soil and fluid mechanics, petroleum and chemical engineers, physicists and scientists in many other disciplines. The development of better numerical simulation techniques in combination with the enormous expansion of computer tools, have enabled numerical simulation of transport phenomena (mass of phases and components, energy etc. ) in porous domains of interest. Before any practical application of the results of such simulations can be used, it is essential that the simulation models have been proven to be valid. In order to establish the greatest possible coherence between the models and the physical reality, frequent interaction between numericians, mathematicians and the previously quoted researchers, is necessary. Once this coherence is established, the numerical simulations could be used to predict various phenomena such as water management, propagation of pollutants etc. These simulations could be, in many cases, the only financially acceptable tool to carry out an investigation. Current studies within various fields of applications include not only physical comprehension aspects of flow and energy or solute transport in saturated or unsaturated media but also numerical aspects in deriving strong complex equations. Among the various fields of applications generally two types of problems can be observed. Those associated with the pollution of the environment and those linked to water management. The former are essentially a problem in industrialized countries, the latter are a major source of concern in North-Africa.

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This volume focuses on recent advances in the modelling of flow and transport in porous media. The first two sections deal with new model approaches and mathematical methods, including error estimates for approximate solutions, parameter sensitivity studies, and solution techniques for degenerate parabolic equations. The third section addresses mass transport and heat transfer in porous media. The final section covers multi-phase flow and multi-component transport. Model applications are linked to water management and pollution problems and include unsaturated as well as saturated soils, saltwater intrusions into coastal aquifers and contaminant dispersion. The key reference provided at the end of each chapter provides the reader with entry points for further detailed study. This book offers essential reading for civil, environmental and hydraulic engineers involved in management of aquifers through numerical simulations. It also provides faculty and graduate students with recent developments in porous media modelling.

Contenu
I Mathematical methods.- Convergence of a finite volume scheme for a parabolic degenerate equation.- Error estimate for the finite volume approximate of the solution to a nonlinear convective equation.- An error estimate for the approximate solution of a porous media diphasic flow equation.- An analogue of Schwarz's method for the construction of the Green function of the Zaremba problem and its application in underground hydrodynamics.- II New approaches.- Size and double-layer effects on the macroscopic behaviour of clays.- Parameter's sensitivity in water storage modelling for unsaturated soils.- Mathematical investigation for groundwater pollution.- Solution of degenerate parabolic problems by relaxation schemes.- III Mass transport and heat transfer.- Transport in saturated porous media.- Perfection of the simulation of fresh-water / saltwater interface motion.- Numerical dispersivity in modelling of saltwater intrusion into a coastal aquifer.- Theoretical study and experimental validation of transport coefficients for hydrocarbon pollutants in aquifers.- Heat and mass transfer in cylindrical porous medium of activated carbon and ammonia.- Transcient natural convection in a square porous cavity submitted to different time-dependent heating modes.- IV Multiphase studies.- Adaptive mesh for two-phase flow in porous media.- Upscaling two-phase flow in double porosity media: nonuniform homogenization.- Flow of multicomponent gas condensate mixtures in fractured porous media.- Two-scale percolation difference method for simulation the transport with trapping in porous media.- Contributors.