Reply to comment by T. R. Ginn on “Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab”

Abstract

[1] We agree that variable fluid density may materially contribute to 3-D flow effects. This has been investigated under a variety of boundary conditions by a number of researchers [e.g., Schincariol and Schwartz, 1990; Schincariol, 1998; Welty and Gelhar, 1991; Welty et al., 2003] and recently in a very systematic set of simulations for Henry's [1964] saltwater intrusion problem by Kerrou and Renard [2010]. One must bear in mind that the effects of buoyancy differences are enhanced by homogeneity, low Peclet numbers, and distant boundaries. These conditions allow convection cells to develop. Conversely, material heterogeneity, large mean advection perpendicular to the gravity gradient, and closely spaced no-flow boundaries tend to destroy convection and the effects of buoyancy. All of these things are present in the experiment by Klise et al. [2008], so one cannot apply “rules of thumb” from other experiments. More recently, Alkindi et al. [2011] performed similar gravity-stable displacement experiments in a slab of homogeneous beads oriented both flat and vertical and found modest changes to longitudinal dispersion and no reported tailing effects, with very large density differences in resident and displacing fluids. [2] We also point out that the scaling of dispersivity was not the only reason that the classical advection-dispersion equation underperformed in Klise et al.'s [2008] experiment. Most notably, the breakthrough curve tails decayed with a power law of time at all transects, an effect that would not be explained by density effects at the small transport distances. [3] However, including gravity effects could motivate a very interesting paper, if the density-dependent transport was rigorously and simultaneously compared to the other effects that were investigated by Klise et al. [2008] and Major et al. [2011]. We invite the readership to perform a study in the spirit of Major et al. [2011] using the entire measured permeability distribution and a benchmarked code such as SUTRA [Voss and Souza, 1987; Voss and Provost, 2010] that also includes the effects of multirate mass transfer with an immobile phase. We are not aware of such a code. One must also take care to accurately represent the highly variable velocity field because of the influence of the velocity vector error on fluid mixing [Benson et al., 1998].