Scale-dependent hydraulic conductivity in anisotropic media from dimensional cross-over

A cross-over from 1D conduction to 3D conduction with increasing scale is shown to account for the kind of scale-dependent hydraulic conductivity sometimes observed in anisotropic systems. The cross-over is investigated in the context of the application of continuum percolation theory to a random fractal model. The dimensional cross-over is defined in terms of a comparison between the correlation length from percolation theory and the system dimensions.RésuméLe passage d’une conductivité 1D à une conductivité 3D, avec une échelle d’étude croissante, est étudié de manière à supputer les dépendances de la conducticité hydraulique aux échelles, parfois observées dans les systèmes anisotropiques. Ce passage est investigué dans le contexte d’une application de la théorie de la percolation continue à un modèle fractal probabiliste. Le passage dimensionnel est définit en terme de comparaison entre la longueur de corrélation issue de la théorie de la percolation, et les dimensions du système.ResumenSe muestra un cruce de conducción en 1D a conducción 3D con escala creciente para explicar el tipo de conductividad hidráulica dependiente de escala que se observa algunas veces en sistemas anisotrópicos. Se investiga el cruce en el contexto de la aplicación de la teoría de percolación continua a un modelo fractal aleatorio. El cruce dimensional se define en términos de una comparación entre la longitud de correlación de la teoría de percolación y las dimensiones del sistema.

[1]  A. Hunt.  Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity , 2003 .

[2]  Dirk Schulze-Makuch,et al.  Scale Dependency of Hydraulic Conductivity in Heterogeneous Media , 1999 .

[3]  Y. Bernabé,et al.  Permeability fluctuations in heterogeneous networks with different dimensionality and topology , 2003 .

[4]  Schwartz,et al.  Structural and dynamical properties of long-range correlated percolation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[5]  W. E. Soll,et al.  Pore scale study of flow in porous media: Scale dependency, REV, and statistical REV , 2000 .

[6]  Yannis C. Yortsos,et al.  The permeability of strongly disordered systems , 1996 .

[7]  Y. Bernabé,et al.  Effect of the variance of pore size distribution on the transport properties of heterogeneous networks , 1998 .

[8]  Sally M. Benson,et al.  Dynamics of fluids in fractured rock , 2000 .

[9]  Daniel M. Tartakovsky,et al.  Theoretical interpretation of a pronounced permeability scale effect in unsaturated fractured tuff , 2002 .

[10]  D. Cherkauer,et al.  Scale Dependency of Hydraulic Conductivity Measurements , 1995 .

[11]  STEADY‐STATE INFILTRATION AS A FUNCTION OF MEASUREMENT SCALE , 1994 .

[12]  Vincent C. Tidwell,et al.  Laboratory method for investigating permeability upscaling , 1997 .

[13]  Garrison Sposito,et al.  Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory , 1991 .

[14]  James J. Butler,et al.  Relationship Between Pumping‐Test and Slug‐Test Parameters: Scale Effect or Artifact? , 1998 .

[15]  Daniel M. Tartakovsky,et al.  Effective Hydraulic Conductivity of Bounded, Strongly Heterogeneous Porous Media , 1996 .

[16]  J. M. Hammersley,et al.  Critical Percolation Probabilities (Bond Problem) , 1961 .

[17]  G. Teutsch,et al.  Effects of the investigation scale on pumping test results in heterogeneous porous aquifers , 1994 .

[18]  M. Pollak,et al.  The Hall effect in the variable-range-hopping regime , 1981 .

[19]  Daniel M. Tartakovsky,et al.  Transient effective hydraulic conductivities under slowly and rapidly varying mean gradients in bounded three‐dimensional random media , 1998 .

[20]  Kang-Kun Lee,et al.  Analysis of the Quality of Parameter Estimates from Repeated Pumping and Slug Tests in a Fractured Porous Aquifer System in Wonju, Korea , 1999, Ground water.

[21]  G. Campbell,et al.  Characterization of Particle-Size Distribution in Soils with a Fragmentation Model , 1999 .

[22]  Thompson,et al.  Quantitative prediction of permeability in porous rock. , 1986, Physical review. B, Condensed matter.

[23]  S. P. Neuman,et al.  Flow in multiscale log conductivity fields with truncated power variograms , 1998 .

[24]  Allen G. Hunt,et al.  Applications of percolation theory to porous media with distributed local conductances , 2001 .

[25]  Chin-Fu Tsang,et al.  Flow channeling in strongly heterogeneous porous media: A numerical study , 1994 .

[26]  S. Friedman,et al.  Critical path analysis of the relationship between permeability and electrical conductivity of three‐dimensional pore networks , 1998 .

[27]  New perspective on the Vedernikov Number , 1991 .

[28]  M. Pollak.  A percolation treatment of dc hopping conduction , 1972 .

[29]  Allen G. Hunt,et al.  Ac hopping conduction: Perspective from percolation theory , 2001 .

[30]  Allen G. Hunt,et al.  Upscaling in Subsurface Transport Using Cluster Statistics of Percolation , 1998 .

[31]  Ioannis Chatzis,et al.  The effect of spatial correlations on the accessibility characteristics of three‐dimensional cubic networks as related to drainage displacements in porous media , 1993 .

[32]  Brian R. Zurbuchen,et al.  Support volume and scale effect in hydraulic conductivity: Experimental aspects , 2000 .

[33]  K. Bradbury,et al.  Hydraulic Conductivity Determinations in Unlithified Glacial and Fluvial Materials , 1990 .

[34]  M. A. García-Vera,et al.  Inverse modeling of groundwater flow in the semiarid evaporitic closed basin of Los Monegros, Spain , 1998 .

[35]  Jesús Carrera,et al.  Scale effects in transmissivity , 1996 .

[36]  Characteristic pore sizes and transport in porous media. , 1987, Physical review. B, Condensed matter.

[37]  Vittorio Di Federico,et al.  Scaling of random fields by means of truncated power variograms and associated spectra , 1997 .

[38]  Vinay Ambegaokar,et al.  Hopping Conductivity in Disordered Systems , 1971 .

[39]  M. Sahimi.  Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing , 1993 .

[40]  Alexander L. Efros,et al.  Electronic Properties of Doped Semi-conductors , 1984 .

[41]  C. H. Seager,et al.  Percolation and conductivity: A computer study. II , 1974 .

[42]  D. Stauffer.  Scaling Theory of Percolation Clusters , 1979, Complex Media and Percolation Theory.

[43]  G. Gee,et al.  Water-Retention of Fractal Soil Models Using Continuum Percolation Theory: Tests of Hanford Site Soils , 2002 .

[44]  S. P. Neuman,et al.  Anisotropy, lacunarity, and upscaled conductivity and its autocovariance in multiscale random fields with truncated power variograms , 1999 .

[45]  Dirk Schulze-Makuch,et al.  Variations in hydraulic conductivity with scale of measurement during aquifer tests in heterogeneous, porous carbonate rocks , 1998 .

[46]  G. Gee,et al.  Application of critical path analysis to fractal porous media: comparison with examples from the Hanford site , 2002 .

[47]  Vincent C. Tidwell,et al.  Heterogeneity, permeability patterns, and permeability upscaling: Physical characterization of a block of Massillon sandstone exhibiting nested scales of heterogeneity , 2000 .

[48]  P. Doussal.  Permeability versus conductivity for porous media with wide distribution of pore sizes. , 1989 .

[49]  W. Brace.  Permeability of crystalline rocks: New in situ measurements , 1984 .