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Correspondence of the Gardner and van Genuchten–Mualem relative permeability function parameters
Author(s) -
Ghezzehei Teamrat A.,
Kneafsey Timothy J.,
Su Grace W.
Publication year - 2007
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 - 10.1029/2006wr005339
Subject(s) - saturation (graph theory) , permeability (electromagnetism) , relative permeability , mathematics , function (biology) , soil science , environmental science , geotechnical engineering , geology , porosity , chemistry , combinatorics , biochemistry , evolutionary biology , membrane , biology
The Gardner and van Genuchten–Mualem models of relative permeability are widely used in analytical and numerical solutions to flow problems, respectively. Comparison of analytical and numerical solutions therefore requires defining some correspondence between the Gardner and van Genuchten–Mualem models. In this paper, we introduce generalized conversion formulae that reconcile these two models in the midrange of saturation. In general, we find that the Gardner parameter α G is related to the van Genuchten parameters α vG and n as α G ≈ 1.3 α vG n . The performance of the proposed conversion formulae is poor when n is much smaller than 2.