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Dynamic effective properties of heterogeneous geological formations with spherical inclusions under periodic time variations
Author(s) -
Rabinovich A.,
Dagan G.,
Miloh T.
Publication year - 2013
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/grl.50319
Subject(s) - dimensionless quantity , thermal conduction , matrix (chemical analysis) , conductivity , physics , flow (mathematics) , electrical resistivity and conductivity , mechanics , thermodynamics , geology , materials science , quantum mechanics , composite material
In unsteady groundwater flow (or similar processes of heat/electrical conduction), the heterogeneous medium structure is characterized by two random properties, the conductivity K and the specific storativity S . The average head field ⟨ H ⟩and the associated effective properties K ef , S ef are determined for a layer with a periodic head drop between boundaries, such that H is periodic in time, and a medium made up of a matrix with a dilute concentration of spherical inclusions. In the common quasi‐steady approximation, K ef is equal to the classical steady solution while S ef = S A , the arithmetic mean. We derive expressions for the frequency dependent K ef , S ef , which are generally complex, i.e., dynamic. The main result is the delineation of the ranges of the parameters: dimensionless frequency ( ω ) and contrasts of conductivity ( κ ) and storativity ( s ) between the matrix and the inclusions, for which dynamic effects are significant.