Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches

TLDR: In this paper, the authors present a review of the history of percolation processes in porous media and fracture models of porous media, including a brief overview of the current state of the art.

Abstract: Part 1 Continuum versus discrete models: a hierarchy of heterogeneities and length scales long-range correlations, fractals and percolation continuum versus discrete models. Part 2 The equations of change: the equation of continuity the momentum equation the diffusion and convective-diffusion equations. Part 3 Fractal concepts and percolation theory: box-counting method and self-similar fractals self-affine fractals multifractal systems fractional Brownian motion and long-range correlations percolation processes a glance at history. Part 3 Diagenetic processes and formation of rock: diagenetic and metasomatic processes continuum models of diagenetic processes geometrical models of diagenetic processes in granular rock a geometrical model of carbonate rock diagenetic processes of fractured rock. Part 5 Morphology of porous media and fractured rock: porosity, specific surface area and tortuosity fluid saturation, capillary pressure and contact angle pore size distribution topological properties of porous media fractal properties of porous media porosity and pore size distribution of fractal porous media morphology of fractured rocks. Part 6 Models of porous media: models of macroscopic porous media models of pore surface roughness models of megascopic porous media interpolation schemes and conditional simulation. Part 7 Models of fractured rock: continuum approach - the multi-porosity models network models simulated annealing model synthetic fractal models mechanical fracture models. Part 8 Flow and transport in porous media: the volume-averaging method and derivation of Darcy's law the Brinkman and Forchheimer equations predicting the permeability, conductivity and diffusivity fractal transport and non-local formulation of diffusion derivation of Archie's law relation between permeability and electrical conductivity relation between permeability and nuclear magnetic resonance dynamic permeability. Part 9 Dispersion in porous media: the phenomenon of dispersion mechanisms of dispersion processes the convective-diffusion equation measurement of dispersion coefficients dispersion in simple systems dependence of dispersion coefficients on the Peclet number models of dispersion in macroscopic porous media long-time tails - dead-end pores versus disorder dispersion in short porous media dispersion in porous media with percolation disorder dispersion in megascopic porous media dispersion in stratified porous media. Part 10 Flow and dispersion in fractured rock: flow in a single fracture - continuum and discrete models flow in fractured rock dispersion in a single fracture dispersion in fractured rock. Part 11 Miscible displacements: factors affecting miscible displacement processes viscous fingering continuum models of miscible displacements in Hele-Shaw cells continuum models of miscible displacements in porous media. (Part contents).