Non‐Fickian transport in homogeneous unsaturated repacked sand

Abstract

[1] It is commonly assumed a priori that solute transport experiments conducted in homogeneously repacked laboratory columns can be described by the advective-dispersive (AD) or single-rate mobile-immobile (MIM) transport model. To investigate this, nonreactive transport through macroscopically homogeneous repacked unsaturated sand was studied at two water contents using laboratory columns of diameter of 11 cm and lengths of 10, 20, and 40 cm. Non-Fickian behavior was found to dominate transport at this scale, with long breakthrough curve (BTC) tailing persistent over the range of column lengths tested. Measured BTC tails were well described by the single-rate MIM model at each depth; however, over the range of travel distances studied BTC tailing was better explained as a result of stochastic-convective (SC) transport or continuous time random walk (CTRW). The SC model was applied using the BTC measured at 10 cm as the probability density function to make predictions to subsequent depths. The CTRW model spreading parameter (b) remained approximately constant across the range of both travel distances and water contents considered. It is concluded that the assumption of a single-rate MIM model cannot be made a priori for macroscopically homogeneous unsaturated sands. In this case, variability between replicates prevented identification of whether a SC transfer function or CTRW provided the best description of transport. These results demonstrate the variability in transport as a result of heterogeneities in column packing, even for macroscopically homogeneous sand, and emphasize the importance of studying transport over a range of travel distances in order to allow prediction of transport.

Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column

“…These phenomena are referred to as anomalous or non-Fickian transport (Berkowitz et al, 2002), and CDE cannot describe it adequately (Levy and Berkowitz, 2003;Berkowitz et al, 2006). Such anomalous phenomena even can be found during solute transport in repacked homogeneous soil column or sandbox (e.g., Padilla et al, 1999;Levy and Berkowitz, 2003;Bromly and Hinz, 2004;. Another problem of CDE is the well recognized scale-dependent dispersion, i.e., the estimated dispersion coefficient or dispersivity is not constant but rather varies with spatial and/or temporal scales (Gelhar et al, 1992).…”

“…Among the transfer function models, the most widely used is the convective lognormal transfer function model (CLT) in which the pdf is assumed to be lognormal. Whereas CDE assumes complete lateral mixing of solutes during transport, the CLT neglects the lateral mixing (Bromly and Hinz, 2004). The CLT has been successfully applied to both laboratory columns (e.g., Zhang et al, 1994;Vanderborght et al, 1996Vanderborght et al, , 1997Bromly and Hinz, 2004) and field tracer tests (e.g., Jury and Roth, 1990).…”

“…This kind of transport can in general be represented by a joint probability density function w(s, t), which describes each particle transition over a distance and direction s in time t (Berkowitz et al, 2006). The CTRW has been used to quantify laboratory tracer tests (Berkowitz et al, 2000Levy and Berkowitz, 2003;Bromly and Hinz, 2004;Cortis et al, 2006;Xiong et al, 2006; and field tracer migration Scher, 1997, 1998;.…”

Effective models for reactive flow under a dominant Péclet number and order one Damköhler number: Numerical simulations

“…The characteristic diffusion D c is then such that σ(t) ∼ √ D c t. Nevertheless, observations have emphasized the existence of regimes where σ rather expands as t α , α = 1/2 (see for instance the observations in a sand column described in [8]). This phenomenon is referred to as anomalous diffusion.…”

“…The crucial difference between problem (6)- (8) and the the one originally considered by Taylor is the boundary condition on the side walls Γ * = {(x * , y * ) : x * ∈ R, |y * | = H}. Taylor assumed no-flux conditions.…”