When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields

Abstract

[1] We describe the upscaled groundwater flow and solute transport characteristics of two-dimensional hydraulic conductivity fields with three fundamentally different spatial textures and consider the conditions under which physical mobile-immobile domain mass transfer occurs in these fields. All three fields have near-identical lognormal univariate conductivity distributions, as well as near-identical isotropic spatial covariance functions. They differ in the pattern by which high-or low-conductivity regions are connected: the first field has connected high-conductivity structures; the second is multivariate logGaussian and, hence, has connected structures of intermediate value; and the third has connected regions of low conductivity. We find substantially different flow and transport behaviors in the three different fields. Flow and transport in the multivariate log-Gaussian field are consistent with stochastic theory. The field with connected high-conductivity paths has an effective conductivity greater than the geometric mean and large variations in fluid velocity. It produces significant mass transfer behavior (i.e., tailing) when the conductivity variance is large and, depending on the system parameters, this mass transfer is driven by either diffusion or advection. In the field with connected low-conductivity regions, the effective conductivity is below the geometric mean and transport is well characterized by the advection-dispersion model with a dispersivity smaller than that in the multivariate log-Gaussian field. Thus, physical mobile-immobile domain mass transfer may occur in smooth hydraulic conductivity fields with univariate log-Gaussian density functions if the variability in conductivity is sufficient and the high values are more connected than modeled by the multivariate log-Gaussian distribution.

Probabilistic human health risk assessment of degradation‐related chemical mixtures in heterogeneous aquifers: Risk statistics, hot spots, and preferential channels

“…The spatial heterogeneity of the hydrogeological properties will dictate the relative importance of the degradation products to the total human health risk. In this context, the variability of the hydraulic properties typically leads to preferential flow channels and lowpermeability areas where contaminants can be temporarily trapped by rate-limited mass transfer [e.g., Gomez-Hernandez and Wen, 1998;Zinn and Harvey, 2003;Bianchi et al, 2011]. The formation of these fast flow channels is typically associated with the presence of well-connected, highly permeable geological bodies or structures that can concentrate flow and solute transport [e.g., Knudby and Carrera, 2005; Incorporating hydrogeological uncertainty in human health predictions has been a topic of intense research in the past [e.g., Andričević and Cvetković, 1996;de Barros and Rubin, 2008;Cvetković and Molin, 2012;Rodak and Silliman, 2011;Andričević et al, 2012;Siirila and Maxwell, 2012;Atchley et al, 2013;de Barros and Fiori, 2014].…”

Effects of intraborehole flow on groundwater age distribution

“…Estimates of regional-scale transport characteristics must incorporate smaller-scale variability into models of the system (some examples of upscaling methods include Gelhar and Axness 1983;Li et al 1994;Haggerty and Gorelick 1995;Berkowitz et al 2000;Haggerty et al 2000). Studies have shown that accurate upscaled transport modeling often requires detailed knowledge of the magnitude and the structure of small-scale heterogeneity (e.g., Goltz and Roberts 1987;Li et al 1994;Di Federico et al 1999;LaBolle and Fogg 2001;Becker and Shapiro 2001;Guswa and Freyberg 2002;Zinn and Harvey 2003;Liu et al 2004;Zinn et al 2004).…”

Random Mixing: An Approach to Inverse Modeling for Groundwater Flow and Transport Problems

“…However, the spatial dependence of the hydraulic transmissivity field W (x) might differ from Gaussian. For example, Zinn and Harvey (2003) showed how different spatial patterns of connectivity lead to different flow and transport behavior, even though the fields applied share the same basic statistics, i.e., the same first and second moment. In Haslauer et al (2012), it was shown that the spatial dependence of transmissivities cannot be described adequately using a Gaussian copula.…”