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Theoretical Insight Into the Empirical Tortuosity‐Connectivity Factor in the Burdine‐Brooks‐Corey Water Relative Permeability Model
Author(s) -
Ghanbarian Behzad,
Ioannidis Marios A.,
Hunt Allen G.
Publication year - 2017
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2017wr021753
Subject(s) - tortuosity , exponent , scaling , statistical physics , relative permeability , porous medium , power law , permeability (electromagnetism) , percolation theory , percolation (cognitive psychology) , saturation (graph theory) , conductivity , mathematics , physics , materials science , porosity , geotechnical engineering , geology , geometry , statistics , chemistry , combinatorics , philosophy , linguistics , biochemistry , neuroscience , membrane , biology , quantum mechanics
A model commonly applied to the estimation of water relative permeability k rw in porous media is the Burdine‐Brooks‐Corey model, which relies on a simplified picture of pores as a bundle of noninterconnected capillary tubes. In this model, the empirical tortuosity‐connectivity factor is assumed to be a power law function of effective saturation with an exponent ( μ ) commonly set equal to 2 in the literature. Invoking critical path analysis and using percolation theory, we relate the tortuosity‐connectivity exponent μ to the critical scaling exponent t of percolation that characterizes the power law behavior of the saturation‐dependent electrical conductivity of porous media. We also discuss the cause of the nonuniversality of μ in terms of the nonuniversality of t and compare model estimations with water relative permeability from experiments. The comparison supports determining μ from the electrical conductivity scaling exponent t , but also highlights limitations of the model.