Comment on “Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab” by E. D. Major et al.


Corresponding author: T. R. Ginn, Civil and Environmental Engineering, UC Davis, Davis, CA 95616, USA. (

[1] The experimental results of Klise et al. 2008 have been the focus of intense discussion about the invalidity of the advection-dispersion equation (ADE) to represent transport processes in natural porous media [Klise et al., 2008; Major et al., 2011; Fiori et al., 2012; Benson et al., 2012] even with significant characterization of the hydraulic conductivity, here via air permeability sampling. All these efforts to quantitatively simulate the transport have ignored the role of density differences between the displaced and the displacing solution. In the tracer experiment, the 30.5 cm × 30.5 cm × 2.1 cm slab of Massillon sandstone was saturated with potassium iodide (KI)-bearing water (0.79 M, Klise, personal communication) and then flushed with deionized water in a linear flood. Solute concentration profiles were taken by X-ray images through the vertical (2.1 cm thickness) dimension at various times, and transient resident concentrations on four transects, derived from the X-ray images, are also reported by Klise et al. [2009].

[2] The tracer test of Klise et al. [2009] involves total tracer (I-) concentration of 100,000 mg/L in the displaced fluid (Klise, personal communication). Istok and Humphrey [1995], in a study of the role of tracer-induced density effects on transport, note “… the possibility of buoyancy-induced flow must be considered when interpreting tracer tests conducted with anion concentrations as low as 50 mg/L.” Murphy et al. [1997] report significant density effects in transport in a heterogeneous sandbox experiment at 50 mg/L and via modeling at solution densities below 1.001 g/mL. The solution density for the initial solute concentration of the experiment of Klise et al. [2009] is 1.093 g/mL [Lide, 2010]. Based on the literature, it appears that density effect may play a role in the transport results of Klise et al. [2009]. More to the point, density effects may induce enhanced spreading that can be misinterpreted as scale-dependent dispersion; Istok and Humphrey [1995] point out regarding density effects in their horizontal radial flow experiments: “The dynamic collapse of the Br-plume caused by buoyancy forces resulted in increased apparent transverse and longitudinal dispersivities.” Major et al. [2011] see dispersion increasing with scale in the Klise et al. [2009] data, as they note “The optimized parameters in the ADE were found to scale predictably, most notably the longitudinal dispersivity (αL), which grew linearly with upscaling,” but they attribute the phenomenon to temporal nonlocality of transport, not to density effects. In conclusion, the debate [Klise et al., 2009; Major et al., 2011; Fiori et al., 2012; Benson et al., 2012] about the validity or lack thereof of the ADE in application to the experimental results of Klise et al. [2009] should be revisited with consideration of alternative processes such as density effects associated with the solute concentration differences.