A solute flux approach to transport in heterogeneous formations: 2. Uncertainty analysis

Abstract

Uncertainty in the mass flux for advection dominated solute movement in heterogeneous porous media is investigated using the Lagrangian framework developed in paper 1 by Dagan et al. (this issue). Expressions for the covariance of the mass flux and cumulative mass flux are derived as functions of the injection volume and sampling area size relative to the scale of heterogeneity. The result is illustrated for solute advection in three types of heterogeneous porous media: stratified formations, two‐ and three‐dimensional porous media; small perturbation approximation is used for the two‐ and three‐dimensional cases. Variances of the mass flux and cumulative mass flux are evaluated as functions of the injection volume (area) scale versus log‐hydraulic conductivity integral scale. The greatest decrease in coefficient of variation (CV) of the mass flux is for the source scale 1–5 times the hydraulic conductivity integral scale; further increase in the source size decreases CV comparatively less. The variance of the cumulative mass flux (or total discharge) indicates that for the source size of 20 hydraulic conductivity integral scales, the transport conditions are almost ergodic. The present results also indicate that the cumulative mass flux is a relatively robust quantity for describing field‐scale solute transport.

A general real-time formulation for multi-rate mass transfer problems

“…In solute transport, non-equilibrium has been attributed to diffusion-limited storage into immobile regions, kinetic sorption or heterogeneity (Brusseau et al, 1989;Sudicky, 1989Sudicky, , 1990Valocchi, 1990;Sardin et al, 1991;Cvetkovic et al, 1992;Toride et al, 1993;Tsang, 1995;Haggerty and Gorelick, 1995;Ray et al, 1997;Carrera et al, 1998;Dentz and Berkowitz, 2003;El-Zein et al, 2005;Salamon et al, 2006;Vogel et al, 2006;Zhang et al, 2006Zhang et al, , 2007Alcolea et al, 2008;Willmann et al, 2008;Kumar, 2008;Gouze et al, 2008). Non-equilibrium is intrinsically associated to multicomponent reactive transport at the field scale (Willmann et al, 2009).…”

Diffuse hydrological mass transport through catchments: scenario analysis of coupled physical and biogeochemical uncertainty effects

“…Over the last decades, many successive publications have quantified different types of uncertainty and investigated their implications for the modelling and management of water pollution (e.g. Cvetkovic et al, 1992;Andricevic and Cvetkovic, 1996;Batchelor et al, 1998;Eggleston and Rojstaczer, 2000;Gren et al, 2000;Jarsjö et al, 2005). Key sources of uncertainty Published by Copernicus Publications on behalf of the European Geosciences Union.…”

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

“…Starting from the work of Dagan (1989), several analytical solutions have been proposed rendering space-time distributions of (ensemble) mean and variance-covariance of concentrations or trajectories and time-of-residence of conservative solutes in multidimensional porous systems (Cvetkovic et al 1992;Kapoor and Gelhar 1994;Kapoor and Kitanidis 1998;Fiori and Dagan 2000;Vanderborght 2001;Guadagnini et al 2003;Sanchez-Vila and Guadagnini 2005;Riva et al 2006). All of these solutions rely on (different flavors of) the perturbation theory to provide approximations of governing equations and associated solutions.…”