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Apparent Conductivity of Random Composite Formations

Author(s): D. M. Tartakovsky; A. Guadagnini; L. Guadagnini; S. Franzetti

Linked Author(s): Alberto Guadagnini

Keywords: Composite media; Random fields; Moment equations; Effective; Equivalent

Abstract: Permeability of most geologic formations varies erratically in space by orders of magnitude and is often modeled as a random space field. It is often computationally expedient to determine the mean values of state variables (pressure heads, velocity) by replacing spatially varying (random) local conductivities with their effective or apparent counterparts. We explore the concept of apparent parameters for formations with uncertain spatial arrangement of geological facies and hydraulic properties within each facies. Our analysis relies on the composite media theory, which employs random domain decomposition to explicitly account for the separate effects of material and geometric uncertainty on ensemble moments of head and flux. We present a general expression for the apparent conductivity of such media and analyze it in detail for one-dimensional steady flow in a bounded random medium composed of two materials of contrasting hydraulic conductivities. Location of the internal boundary between the two materials is random and normally distributed. The resulting apparent conductivity is compared with approximate perturbation solutions.


Year: 2003

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