Numerical modeling of the role of water and clay content in soils' and rocks' bulk electrical conductivity

Received 23 October 2000revised 1 May 2002;accepted 24June 2002;published25November2002. [1] The influence of clay and water content in the electrical conductivity of rocks and soils has been experimentally established and is expressed by simple empirical laws: the Archie's law and the addition law between volume water conductivity and surface shale conductivity. Two independent numerical modeling techniques, the moment method and the finite difference method, are presented here and are used, first, to verify the agreement between Maxwell's equation based theoretical approaches and the empirical laws and, second, to begin to investigate for a possible effect of the microscopic geometry over macroscopic conductivity. A good agreement between simulation results and Archie's law is obtained when both randomly distributed isotropic and elongated microvolumes of conducting water are considered and a slight difference appears between these two microstructures. For low clay contents in clay-dispersed media, the clay-associated conductivity is shown to be proportional to a specific clay area, which is in good agreement with the addition empirical law.

[1]  H. Waff.  Theoretical considerations of electrical conductivity in a partially molten mantle and implications for geothermometry , 1974 .

[2]  A. Tabbagh.  The response of a three‐dimensional magnetic and conductive body in shallow depth electromagnetic prospecting , 1985 .

[3]  Matthias Jonas,et al.  Mathematical–Physical Reappraisal of Archie's First Equation on the Basis of a Statistical Network Model , 2000 .

[4]  Daniel H. Rothman,et al.  Cellular‐automaton fluids: A model for flow in porous media , 1988 .

[5]  T. Miyamoto,et al.  Effects of Liquid-phase Electrical Conductivity, Water Content, and Surface Conductivity on Bulk Soil Electrical Conductivity1 , 1976 .

[6]  Numerical modeling for electromagnetic remote sensing of inhomogeneities in the ground , 1979, Proceedings of the IEEE.

[7]  Weng Cho Chew,et al.  FREQUENCY DEPENDENT DIELECTRIC AND CONDUCTIVITY RESPONSE OF SEDIMENTARY ROCKS. , 1983 .

[8]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen , 1935 .

[9]  Jie Zhang,et al.  3-D resistivity forward modeling and inversion using conjugate gradients , 1995 .

[10]  W. David Kennedy,et al.  Electrical efficiency -- A pore geometric theory for interpreting the electrical properties of reservoir rocks , 1994 .

[11]  L. Cathles,et al.  Electrical conductivity in shaly sands with geophysical applications , 1998 .

[12]  M. H. Waxman,et al.  Electrical Conductivities in Oil-Bearing Shaly Sands , 1968 .

[13]  P. Glover,et al.  Nature of surface electrical conductivity in natural sands, sandstones, and clays , 1998 .

[14]  J. Mareschal,et al.  Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas , 2000 .

[15]  Tamaz Chelidze,et al.  Electrical spectroscopy of porous rocks: a review—I. Theoretical models , 1999 .

[16]  A. E. Bussian.  Electrical conductance in a porous medium , 1983 .

[17]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[18]  3-D Inversion In Subsurface Electrical Surveying—I. Theory , 1994 .

[19]  Christian Camerlynck,et al.  Numerical modeling for investigating the physical meaning of the relationship between relative dielectric permittivity and water content of soils , 2000 .

[20]  A. Raiche.  An Integral Equation Approach to Three-Dimensional Modelling , 1974 .

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

[22]  Paul W. J. Glover,et al.  A modified Archie’s law for two conducting phases , 2000 .

[23]  G. W. Hohmann.  Three-Dimensional Induced Polarization and Electromagnetic Modeling , 1975 .

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

[25]  Sen,et al.  Dependence of the conductivity of a porous medium on electrolyte conductivity. , 1988, Physical review. B, Condensed matter.

[26]  P. Glover,et al.  Theory of ionic-surface electrical conduction in porous media , 1997 .

[27]  P. N. Sen,et al.  A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads , 1981 .

[28]  Morrel H. Cohen,et al.  The effect of grain anisotropy on the electrical properties of sedimentary rocks , 1982 .

[29]  R. Knight,et al.  Effects of pore structure and wettability on the electrical resistivity of partially saturated rocks—A network study , 1997 .

[30]  D. Parasnis,et al.  Principles of Applied Geophysics , 1962 .

[31]  Pierre M. Adler,et al.  The formation factor of reconstructed porous media , 1992 .

[32]  J. Garnett,et al.  Colours in Metal Glasses and in Metallic Films , 1904 .

[33]  A. Dey,et al.  Resistivity modeling for arbitrarily shaped three-dimensional structures , 1979 .

[34]  K. Spitzer.  A 3-D FINITE-DIFFERENCE ALGORITHM FOR DC RESISTIVITY MODELLING USING CONJUGATE GRADIENT METHODS , 1995 .