Journal
MATHEMATICAL GEOSCIENCES
Volume 44, Issue 2, Pages 133-145Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s11004-011-9365-2
Keywords
Connectivity; Preferential flow; Channeling; Heterogeneous media; Random conductivity; Porous media; Stochastic processes
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This paper analyzes the emergence of channeling and preferential flow in heterogeneous porous media. Connectivity is studied through the statistical characterization of the length L of connected, high velocity patterns in both two-dimensional and three-dimensional media. A simple, physically based, fully analytic expression for the probability of L has been derived. It is found that the length L of connected, high velocity channels is flow-related and can be much larger than the conductivity integral scale I. Heterogeneity has a considerable impact on emergence of channeling patterns; connectivity is considerably enhanced in three-dimensional structures as compared to two-dimensional ones. The strong dependence on space dimensionality is a warning against the use of two-dimensional numerical models for assessing connectivity and preferential flow in heterogeneous media. The probability p(L) is employed in order to determine the early arrivals of the breakthrough curve at a given control plane; the simple model can be used for a preliminary assessment of preferential flow. Comparison with numerical simulations confirms that the main connectivity features were adequately captured by the model.
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