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Temporal moments for transport with mass transfer described by an arbitrary memory function in heterogeneous media
Author(s) -
Luo Jian,
Cirpka Olaf A.,
Dentz Marco,
Carrera Jesus
Publication year - 2008
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 - 10.1029/2007wr006262
Subject(s) - moment (physics) , mass transfer , function (biology) , flux (metallurgy) , mathematics , physics , mathematical analysis , central moment , probability density function , velocity moments , diffusion , transfer function , statistical physics , moment generating function , mechanics , thermodynamics , statistics , classical mechanics , chemistry , quantum mechanics , organic chemistry , wavefront , evolutionary biology , zernike polynomials , electrical engineering , biology , engineering
Temporal moment equations are generalized for transport under linear mass transfer, which has been used to model a broad range of small‐scale processes: kinetic sorption, diffusion into immobile regions, and transport through heterogeneous aquifers. Solving the moment equations, which are formally identical to steady state transport equations, is computationally more efficient than evaluating the temporal moments by integrating the transient flux concentrations. We derive recursive relations for the moments of the flux concentration, which involve the moments of the memory function but do not dependent on its shape. It turns out that two mass transfer models have the same k th temporal moment if the moments of order lower than k are equal. Particularly, the mean retention time, i.e., the first moment of the retention probability density function (pdf) in the immobile domain, decides the second temporal moment of concentration. A mass transfer model with two first‐order rate coefficients can match up to the fourth temporal moment described by a multirate model with a predescribed pdf of the mass transfer rate coefficient. The k th temporal moment is finite when the ( k ‐1)th moment of the memory function exists.