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Comparison of the predictions of universal scaling of the saturation dependence of the air permeability with experiment
Author(s) -
GhanbarianAlavijeh Behzad,
Hunt Allen G.
Publication year - 2012
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 - 10.1029/2011wr011758
Subject(s) - scaling , saturation (graph theory) , exponent , porosity , permeability (electromagnetism) , power law , statistical physics , air permeability specific surface , soil science , mathematics , scaling law , materials science , thermodynamics , physics , environmental science , chemistry , statistics , geometry , composite material , layer (electronics) , membrane , philosophy , linguistics , biochemistry , combinatorics
We compare predictions of the saturation dependence of air permeability from percolation theory with experimental results taken from the last 60 years. We selected experiments with sufficient density of data points to verify a functional dependence. The typical number of such data points was about 10, but actual values ranged from 4 to 31. The predicted saturation dependence is a universal power law in the air‐filled porosity (less a threshold value) with an exponent of 2.00. Our investigation showed that the experimental power was 2.028 ± 0.028 with an R 2 value, averaged across all the experiments, of greater than 0.96 for database 1 (including 16 samples from the literature) and 1.814 ± 0.386 with an R 2 value of larger than 0.90 for database 2 (including 23 samples from Tang et al. (2011)). The threshold value of the air‐filled porosity could be predicted reasonably from the wet end of the soil water retention curves. The threshold varied systematically with soil texture. We also compare the proposed model with three other methods, e.g., Millington and Quirk, Burdine‐Brooks‐Corey, and Kawamoto et al., in estimation of air permeability. The results indicate that the universal scaling approach estimates air permeability more accurately than other methods. Thus, we believe that we have confirmed the universal scaling predicted as well as demonstrated its usefulness in predicting the air permeability.