PERCOLATION THEORY AND ITS APPLICATION TO GROUNDWATER HYDROLOGY

The theory of percolation, originally proposed over 30 years ago to describe flow phenomena in porous media, has undergone enormous development in recent years, primarily in the field of physics. The principal advantage of percolation theory is that it provides universal laws which determine the geometrical and physical properties of the system. This survey discusses developments and results in percolation theory to date, and identifies aspects relevant to problems in groundwater hydrology. The methods of percolation theory are discussed, previous applications of the theory to hydrological problems are reviewed, and future directions for study are suggested.

[1]  Paul J. Flory,et al.  Molecular Size Distribution in Three Dimensional Polymers. I. Gelation1 , 1941 .

[2]  L. E. Scriven,et al.  Percolation and conduction on Voronoi and triangular networks: a case study in topological disorder , 1984 .

[3]  Sen,et al.  Nonuniversal critical exponents for transport in percolating systems with a distribution of bond strengths. , 1985, Physical review. B, Condensed matter.

[4]  J. Straley,et al.  Distribution-induced non-universality of the percolation conductivity exponents , 1979 .

[5]  L. E. Scriven,et al.  Percolation theory of two phase flow in porous media , 1981 .

[6]  Elisabeth Charlaix,et al.  Permeability of a random array of fractures of widely varying apertures , 1987 .

[7]  P. C. Robinson,et al.  Numerical calculations of critical densities for lines and planes , 1984 .

[8]  Paul A. Witherspoon,et al.  The relationship of the degree of interconnection to permeability in fracture networks , 1985 .

[9]  Brian Berkowitz,et al.  Dispersion in Sub‐Representative Elementary Volume Fracture Networks: Percolation Theory and Random Walk Approaches , 1991 .

[10]  P. C. Robinson Connectivity of fracture systems-a percolation theory approach , 1983 .

[11]  P. Doyen,et al.  Permeability, conductivity, and pore geometry of sandstone , 1988 .

[12]  É. Clément,et al.  Scaling Concepts in Porous Media , 1991 .

[13]  A. J. DeGregoria A predictive Monte Carlo simulation of two‐fluid flow through porous media at finite mobility ratio , 1985 .

[14]  A. Suzuki,et al.  Analysis of Radionuclide Transport through Fracture Networks by Percolation Theory. , 1991 .

[15]  Latino Torelli,et al.  Computer simulation of the dispersion phenomena occurring during flow through porous media, using a random maze model , 1972 .

[16]  L. E. Scriven,et al.  Percolation and conduction on the 3D Voronoi and regular networks: a second case study in topological disorder , 1984 .

[17]  L. E. Scriven,et al.  Displacement of residual nonwetting fluid from porous media , 1981 .

[18]  H. E. Hudson,et al.  FUNDAMENTAL FACTORS GOVERNING THE STREAMLINE FLOW OF WATER THROUGH SAND [with DISCUSSION] , 1933 .

[19]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[20]  Wilkinson,et al.  Percolation effects in immiscible displacement. , 1986, Physical review. A, General physics.

[21]  David B. McWhorter,et al.  The Use of Macroscopic Percolation Theory to Construct Large-Scale Capillary Pressure Curves , 1992 .

[22]  Balberg Excluded-volume explanation of Archie's law. , 1986, Physical review. B, Condensed matter.

[23]  Po‐zen Wong,et al.  The Statistical Physics of Sedimentary Rock , 1988 .

[24]  Muhammad Sahimi,et al.  Statistical and continuum models of fluid-solid reactions in porous media , 1990 .

[25]  B. Berkowitz,et al.  Solute transport in fracture channel and parallel plate models , 1991 .

[26]  Berkowitz,et al.  Analytic derivation of percolation thresholds in anisotropic systems of permeable objects. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[27]  T. Madden Random Networks and Mixing Laws , 1976 .

[28]  F. Dullien,et al.  Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network , 1987 .

[29]  Scott Kirkpatrick,et al.  An introduction to percolation theory , 1971 .

[30]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[31]  M. Sahimi,et al.  A percolation model of catalyst deactivation by site coverage and pore blockage , 1985 .

[32]  D. Wilkinson,et al.  Monte Carlo study of invasion percolation clusters in two and three dimensions , 1984 .

[33]  C. Harris Application of generalised effective-medium theory to transport in porous media , 1990 .

[34]  J. Hammersley,et al.  Percolation Processes and Related Topics , 1963 .

[35]  S. Silliman The influence of grid discretization on the percolation probability within discrete random fields , 1990 .

[36]  Brian Berkowitz,et al.  Percolation approach to the problem of hydraulic conductivity in porous media , 1992 .

[37]  J. Dienes,et al.  Transport properties of rocks from statistics and percolation , 1989 .

[38]  Emil O. Frind,et al.  An overview of immiscible fingering in porous media , 1988 .

[39]  A. Aharony Anomalous Diffusion on Percolating Clusters , 1983 .

[40]  Feng,et al.  Transport properties of continuum systems near the percolation threshold. , 1987, Physical review. B, Condensed matter.

[41]  Wilkinson,et al.  Transport and dispersion in random networks with percolation disorder. , 1988, Physical review. A, General physics.

[42]  N. Rivier,et al.  A criterion for percolation threshold in a random array of plates , 1984 .

[43]  Joel Koplik,et al.  Capillary displacement and percolation in porous media , 1982, Journal of Fluid Mechanics.

[44]  Isaac Balberg,et al.  Excluded volume and its relation to the onset of percolation , 1984 .

[45]  Muhammad Sahimi Hydrodynamic dispersion near the percolation threshold: scaling and probability densities , 1987 .

[46]  E. T. Gawlinski,et al.  Monte-Carlo renormalisation group for continuum percolation with excluded-volume interactions , 1983 .

[47]  Feng,et al.  Differences between lattice and continuum percolation transport exponents. , 1985, Physical review letters.

[48]  A. Katz,et al.  Prediction of rock electrical conductivity from mercury injection measurements , 1987 .

[49]  G. Marsily,et al.  Water penetration through fractured rocks: Test of a tridimensional percolation description , 1985 .

[50]  P. Renault,et al.  The effect of spatially correlated blocking-up of some bonds or nodes of a network on the percolation threshold , 1991 .

[51]  L. Sander,et al.  Diffusion-limited aggregation , 1983 .

[52]  Ioannis Chatzis,et al.  The modeling of mercury porosimetry and the relative permeability of mercury in sandstones using percolation theory , 1985 .

[53]  David Wilkinson,et al.  Invasion percolation: a new form of percolation theory , 1983 .

[54]  M. Sahimi,et al.  Stochastic transport in disordered systems , 1983 .

[55]  Norman C. Wardlaw,et al.  Pore-throat size correlation from capillary pressure curves , 1987 .

[56]  On diffusion in fractal porous media , 1991 .

[57]  D. E. Elrick,et al.  Percolation processes and porous media: I. Geometrical and topological model of porous media using a three-dimensional joint pore size distribution , 1986 .

[58]  Yves Guéguen,et al.  Effective medium theory and network theory applied to the transport properties of rock , 1990 .

[59]  M. Yanuka,et al.  Percolation processes and porous media: II. Computer calculations of percolation probabilities and cluster formation , 1989 .

[60]  A. H. Thompson,et al.  The microgeometry and transport properties of sedimentary rock , 1987 .

[61]  Tamaz Chelidze,et al.  Percolation and fracture , 1982 .

[62]  Mukul M. Sharma,et al.  Application of percolation theory to noncatalytic gas‐solid reactions , 1984 .

[63]  Benjamin Ross Dispersion in Fractal Fracture Networks , 1986 .

[64]  R. Lenormand Pattern growth and fluid displacements through porous media , 1986 .

[65]  G. E. Archie The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[66]  Scott W. Tyler,et al.  An explanation of scale‐dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry , 1988 .

[67]  G. R. Jerauld,et al.  The effect of pore-structure on hysteresis in relative permeability and capillary pressure: Pore-level modeling , 1990 .

[68]  Ramon G. Bentsen,et al.  An extended theory to predict the onset of viscous instabilities for miscible displacements in porous media , 1990 .

[69]  M. Yanuka,et al.  Percolation processes and porous media: III. Prediction of the capillary hysteresis loop from geometrical and topological information of pore space , 1989 .

[70]  L. Paterson,et al.  Diffusion-Limited Aggregation and Two-Fluid Displacements in Porous Media , 1984 .

[71]  J. Dienes PERMEABILITY, PERCOLATION AND STATISTICAL CRACK MECHANICS , 1982 .

[72]  C. Zarcone,et al.  Invasion percolation in an etched network: Measurement of a fractal dimension. , 1985, Physical review letters.

[73]  Isaac Balberg,et al.  Recent developments in continuum percolation , 1987 .

[74]  Clayton V. Deutsch,et al.  Calculating effective absolute permeability in sandstone/shale sequences , 1989 .

[75]  Brian Berkowitz,et al.  Application of a percolation model to flow in fractured hard rocks , 1991 .

[76]  I. Balberg,et al.  Anomalous diffusion and continuum percolation , 1987 .

[77]  Walter H. Stockmayer,et al.  Theory of Molecular Size Distribution and Gel Formation in Branched‐Chain Polymers , 1943 .

[78]  Percolation theory and models of unsaturated porous media , 1980 .

[79]  S. Havlin,et al.  Diffusion in disordered media , 2002 .

[80]  R. Lenormand,et al.  Capillary fingering: Percolation and fractal dimension , 1989 .

[81]  Alon,et al.  Systematic derivation of percolation thresholds in continuum systems. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[82]  W. C. Krumbein,et al.  Permeability as a Function of the Size Parameters of Unconsolidated Sand , 1943 .

[83]  Muhammad Sahimi,et al.  Computer simulation of particle transport processes in flow through porous media , 1991 .

[84]  L. E. Scriven,et al.  Percolation theory of residual phases in porous media , 1977, Nature.

[85]  Muhammad Sahimi,et al.  The effect of morphological disorder on hydrodynamic dispersion in flow through porous media , 1988 .

[86]  D. Vere-Jones,et al.  Statistical theories of crack propagation , 1977 .

[87]  Kevin Hestir,et al.  Analytical expressions for the permeability of random two-dimensional Poisson fracture networks based on regular lattice percolation and equivalent media theories , 1990 .

[88]  Z. Jaeger,et al.  Fluid Flow Through a Crack Network in Rocks , 1983 .

[89]  Joel Koplik,et al.  Conductivity and permeability of rocks , 1984 .

[90]  M. Celia,et al.  The effect of heterogeneity on the drainage capillary pressure‐saturation relation , 1992 .

[91]  Martin J. Blunt,et al.  Relative permeabilities from two- and three-dimensional pore-scale network modelling , 1991 .

[92]  Muhammad Sahimi,et al.  Percolation theory of two-phase relative permeability , 1992 .

[93]  F. Dullien Porous Media: Fluid Transport and Pore Structure , 1979 .

[94]  Wilkinson,et al.  Pore-scale viscous fingering in porous media. , 1985, Physical review letters.

[95]  Alon,et al.  New, heuristic, percolation criterion for continuum systems. , 1991, Physical review letters.

[96]  V. Klemeš,et al.  Dilettantism in hydrology: Transition or destiny? , 1986 .

[97]  Percolation theory approach to transport phenomena in porous media , 1992 .

[98]  Jots - a mathematical model of microscopic fluid flow in porous media , 1990 .

[99]  Yves Guéguen,et al.  Percolation networks and fluid transport in the crust , 1991 .

[100]  Stephen E. Silliman,et al.  Stochastic analysis of paths of high hydraulic conductivity in porous media , 1988 .

[101]  Fluid percolation in bond-site size-correlated three-dimensional networks , 1990 .

[102]  A. Scheidegger,et al.  Random maze models of flow through porous media , 1971 .