Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions?

By M. Willmann, Jesús Carrera, X. Sanchez‐Vila. 2008

144 citations recorded by the source corpus.

Power law tailing is often observed in the breakthrough curves (BTCs) of tracer tests. Tailing is attributed to heterogeneity of aquifer properties and cannot be properly modeled by means of the homogeneous advection‐dispersion equation. Mass transfer models (e.g., continuous time random walk method, multirate mass transfer, or fractional‐order advection‐dispersion equations) using memory have been widely applied for reproducing observed tails. The relationship between memory parameters obtained from BTC fitting and the parameters characterizing the heterogeneity of hydraulic properties is still unclear. Here we investigate the conditions under which heterogeneity produces the type of tailing observed in the field and how memory functions are influenced by measurable heterogeneity parameters (e.g., variance, variogram, or integral scale of the underlying transmissivity field). We find that the slope of a BTC in a log‐log plot is mainly influenced by the connectivity of the underlying permeability field but is insensitive to its variance. The slope BTC reaches asymptotically 2 as connectivity increases. We conclude that an appropriate choice of the memory function allows reproducing the spreading caused by hydraulic heterogeneity but not necessarily the rate of mixing.

Subfields: Environmental Engineering, Geophysics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/2ada6abbdc05ce405fdd0b7b6e01e386abcf21f4

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Citations in the corpus

Connectivity metrics for subsurface flow and transport (2013, background): “[132] have investigated the relations between the transport behavior of a medium and its connectivity metrics.”
Solute transport in low‐heterogeneity sandboxes: The role of correlation length and permeability variance (2014, background): “Various numerical studies have identified connectivity and correlation length as key parameters that determine solute breakthrough [Renard and Allard, 2013; Willmann et al., 2008; Zinn and Harvey, 2003].”
Origins of anomalous transport in heterogeneous media: Structural and dynamic controls (2014, background): “…et al., 2000; Cirpka and Kitanidis, 2000; Cirpka and Surabhin, 2004; Sanchez-Vila and Carrera, 2004; Berkowitz et al., 2006; Morales Casique et al., 2006a, 2006b; Le Borgne et al., 2008; Willmann et al., 2008; Kang et al., 2011; Rubin et al., 2012, and references therein, to mention only a few].”