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Macroscopic Modelling of Transport Phenomena in Porous Media. 1: The Continuum Approach
Yehuda Bachmat,Jacob Bear +1 more
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In this article, the authors present a systematic development of a continuum model of a porous medium and of transport processes occurring in it, and the concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified.Abstract:
This is the first of two papers presenting a systematic development of a continuum model of a porous medium and of transport processes occurring in it. The concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified. A universal criterion for selecting the size of an REV as a function of measurable characteristics of a porous medium and selected tolerance levels of estimation errors, is developed. The rules of spatial averaging are extended by including the effects of both the configuration of the solid matrix and of interphase transfer phenomena within an REV.read more
Citations
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Numerical models and experiments on immiscible displacements in porous media
TL;DR: In this paper, the authors present the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale, and they show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged.
Journal ArticleDOI
Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries
TL;DR: In this paper, a macroscopic thermodynamic theory was developed to describe two-phase flow in porous media, where the authors developed a constitutive theory resulting in balance equations and thermodynamics appropriate for modelling multiphase flow.
Journal ArticleDOI
Fixed grid techniques for phase change problems: A review
TL;DR: In this paper, the major fixed grid formulations and solution methods for conduction controlled phase change problems are categorised using a two phase model of a solid/liquid phase change, the basic enthalpy equation is derived.
Journal ArticleDOI
Nomsothermal multiphase flow of brine and gas through saline media
TL;DR: In this article, a formulación nueva for the analysis of problemas Termo-hidro-mecanicos in medios salinos is presented, which includes, desde the obtencion of ecuaciones de balance of masa, momento, and energia, to its resolucion numerica, including the derivation of algunas ecuación constitutivas.
Journal ArticleDOI
Numerical analysis of hygro-thermal behaviour and damage of concrete at high temperature
TL;DR: In this article, a computational analysis of hygro-thermal and mechanical behavior of concrete structures at high temperature is presented, and the evaluation of thermal, hygral and mechanical performance of this material, including damage effects, needs the knowledge of the heat and mass transfer processes.
References
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Methods of Theoretical Physics. By P.M. Morse and H. Feschbach. 2vols., Pp.xxii, 1978. 120s. each vol. 1953.(McGraw-Hill)
Book
Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
Book
Integral geometry and geometric probability
Abstract: Part I. Integral Geometry in the Plane: 1. Convex sets in the plane 2. Sets of points and Poisson processes in the plane 3. Sets of lines in the plane 4. Pairs of points and pairs of lines 5. Sets of strips in the plane 6. The group of motions in the plane: kinematic density 7. Fundamental formulas of Poincare and Blaschke 8. Lattices of figures Part II. General Integral Geometry: 9. Differential forms and Lie groups 10. Density and measure in homogenous spaces 11. The affine groups 12. The group of motions in En Part III. Integral Geometry in En: 13. Convex sets in En 14. Linear subspaces, convex sets and compact manifolds 15. The kinematic density in En 16. Geometric and statistical applications: stereology Part IV. Integral Geometry in Spaces of Constant Curvature: 17. Noneuclidean integral geometry 18. Crofton's formulas and the kinematic fundamental formula in noneuclidean spaces 19. Integral geometry and foliated spaces: trends in integral geometry.