HR: 17:00h
AN: H14B-05    [Abstracts]
TI: Effective Conductivity of 2D Isotropic Formations: Performance of the Effective Medium Approximation
AU: * Jankovic, I
EM: ijankovi@eng.buffalo.edu
AF: State University of New York at Buffalo, Department of Civil, Structural and Environmental Engineering, Buffalo, NY 14260-4400 United States
AU: Fiori, A
EM: aldo@uniroma3.it
AF: Universita di Roma Tre, Dipartimento di Scienze dell' Ingegneria Civile, Via V. Volterra 62, Roma, 00146 Italy
AB: The effective conductivity of isotropic formations is investigated using a combination of the effective medium approximation and accurate numerical simulations. The 2D isotropic heterogeneous medium contains circular inclusions of uniform radii and of two different conductivities, K1 and K2. The inclusions are submerged into a homogeneous matrix. The matrix conductivity was set to an effective conductivity computed using the effective medium approximation. The matrix represents inclusions of the same conductivities, but of much smaller radii. The conglomerate of inclusions is placed in a circular domain and subject to uniform flow from infinity. The average velocity inside the conglomerate differs from that at infinity. The difference in the velocities is used to infer the actual effective conductivity. For our binary medium, the latter depends on three parameters: the conductivity ratio K1/K2, the total area fraction n of the inclusions and the relative area fraction n1. For n1=0.5 (equal numbers of inclusions of conductivity K1 and K2), the classical Matheron-Dykhne exact result was recovered; the actual effective conductivity equals the geometric mean of inclusions' conductivities. For an asymmetrical distribution (n1 different from 0.5) the effective medium approximation is shown to be quite accurate even for relatively large values of the total area fraction or the log-conductivity variance; the actual effective conductivity and that computed using the effective medium approximation are very close. The cases of a wide conductivity distribution and different radii are briefly discussed.
DE: 1829 Groundwater hydrology
DE: 1831 Groundwater quality
DE: 1832 Groundwater transport
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting