Exploring the nature of non-Fickian transport in laboratory experiments

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 psi(t) similar to t(-1-beta) with 0 < beta < 2 for the spectrum of transition times comprising a tracer plume migration. For each sandbox medium a choice of beta resulted in an excellent fit to the breakthrough curve (BTC) data, and the value of beta decreased slowly with increasing flow velocity. Here, the data are reanalyzed with the full spectrum of psi(t) gleaned from analytical calculations [Cortis A, Chen Y, Scher H, Berkowitz B. Quantitative characterization of pore-scale disorder effects on transport in "homogeneous" granular media. Phys Rev E 2004:10(70):041108. doi:10.1103/PhysRevE.70.0411081, 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 IN 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), psi(t) similar to (t(1) + t)(-1-beta) exp(-t/t(2)), where t(1) and t(2) 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 t(1), beta, t(2). The influence of the cutoff time t(2) is apparent even in the regime t < t(2). Significantly, we demonstrate that the previous apparent velocity dependence of beta is a result of choosing a pure power law tail for psi(t). The key is the change in the log-log slope of the TPL form of psi(t) with a shifting observational time window caused by the change in the mean velocity. Hence, the use of the full spectrum of psi(t) is not only necessary for the transition to Fickian behavior, but also to account for the dynamics of these laboratory observations of non-Fickian transport. (C) 2008 Elsevier Ltd. All rights reserved.