Exploring the nature of non-Fickian transport in laboratory experiments

Abstract Observations of non-Fickian transport in sandbox experiments [Levy M, Berkowitz B. Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 2003;64:203–26] were analyzed previously using a power law tail ψ(t) ∼ t−1−β with 0  doi: 10.1103/PhysRevE.70.041108 ], numerical simulations [Bijeljic B, Blunt MJ. Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour Res 2006;42:W01202. doi: 10.1029/2005WR004578 ] and permeability fields [Di Donato G, Obi E-O, Blunt MJ. Anomalous transport in heterogeneous media demonstrated by streamline-based simulation. Geophys Res Lett 2003;30:1608–12s. doi: 10.1029/2003GL017196 ]. We represent the main features of the full spectrum of transition times with a truncated power law (TPL), ψ(t) ∼ (t1 + t)−1−βexp(−t/t2), where t1 and t2 are the limits of the power law spectrum. An excellent fit to the entire BTC data set, including the changes in flow velocity, for each sandbox medium is obtained with a single set of values of t1, β, t2. The influence of the cutoff time t2 is apparent even in the regime t

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