HR: 0800h
AN: H21L-01 INVITED    [Abstracts]
TI: Relationship between Permeability, Elastic Moduli and Pore Structure in Porous Geological Media
AU: * Zimmerman, R W
EM: robertzi@kth.se
AF: Division of Engineering Geology and Geophysics, Royal Institute of Technology (KTH), Stockholm, 100 44, Sweden
AB: The petrophysical properties of porous media, such as the permeability and the elastic moduli, are essentially controlled by the geometry of the pore space. Enormous amounts of research have been devoted over the past several decades to understanding and quantifying the relationship between pore structure and petrophysical properties (for example, see Zimmerman, Compressibility of Sandstones, 1991; Dullien, Porous Media: Fluid Transport and Pore Structure, 1992; Adler, Porous Media: Geometry and Transports, 1992; Mavko et al., The Rock Physics Handbook, 1998; etc.) Although much is now known in terms of general trends, bounds, etc., the state of knowledge is still such that existing theories can rarely provide accurate numerical estimates of the permeability or bulk modulus of a given rock. To a great extent the problem lies in the fact that micromechanics-based rock physics theories typically utilize idealized pore shapes such as circular, elliptical or triangular cylinders, for which analytical solutions can readily be obtained, whereas actual pores are irregular. In this talk I will describe recent work that utilizes actual pore geometries, as observed in electron micrographs, along with some scaling laws based on the pore areas and perimeters, and simple effective medium approximations, to predict the permeability and elastic moduli of porous sedimentary rocks. The hydraulic conductivity of the individual pores are estimated from the hydraulic radius approximation, which correlates the conductance with area³/perimeter², with the proportionality constant chosen so as to make the relation exact for a circle. Kirkpatrick's effective medium approximation for networks of conductors is used to upscale the individual pore-scale hydraulic conductivities to yield the core-scale permeability. When applied to several data sets of sandstones and carbonates, with permeabilities ranging from 0.5-1500 milliDarcies, the methodology typically predicts the permeability to within a factor of two. The compressibilities of the individual pores are estimated from a scaling law based on perimeter²/area, with the proportionality constant again found from the known case of a circular tube. The individual pore compressibilities are then averaged, weighted by area, and the differential effective medium approximation is used to convert the mean pore compressibility into the macroscopic bulk modulus. This methodology has been applied to Berea and Fontainebleau sandstone, and typically predicts the bulk modulus to within about 10%.
DE: 1810 Debris flow and landslides
DE: 1822 Geomechanics
DE: 1865 Soils (0486)
DE: 1866 Soil moisture
DE: 5114 Permeability and porosity
SC: Hydrology [H]
MN: 2007 Fall Meeting