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A general memory function for modeling mass transfer in groundwater transport
Author(s) -
Cvetkovic Vladimir
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 - 10.1029/2011wr011657
Subject(s) - groundwater , function (biology) , scale (ratio) , mass transfer , mass transport , set (abstract data type) , environmental science , field (mathematics) , soil science , hydrology (agriculture) , computer science , mathematics , mechanics , geotechnical engineering , geology , physics , engineering , biochemical engineering , quantum mechanics , biology , programming language , pure mathematics , evolutionary biology
A power‐law extension of the gamma distribution is proposed as a general memory function for capturing rate limitations of retention in groundwater transport. Using moments, we show how the new memory function can be reduced to most other forms available in the literature, exactly or approximately. The proposed formulation is suitable for field scale or laboratory scale transport modeling. Rate limitation effects are illustrated for solute transport by considering the fractional mass release over a given transport scale. The equilibrium and no‐retention cases set bounds for contaminant attenuation, between which the impact of rate limitations is clearly exposed.