[1] In this paper we present flow and travel time ensemble statistics based on a new simulation methodology, the adaptive Fup Monte Carlo method (AFMCM). As a benchmark case, we considered two-dimensional steady flow in a rectangular domain characterized by multi-Gaussian heterogeneity structure with an isotropic exponential correlation and lnK variance s Y 2 up to 8. Advective transport is investigated using the travel time framework where Lagrangian variables (e.g., velocity, transverse displacement, or travel time) depend on space rather than on time. We find that Eulerian and Lagrangian velocity distributions diverge for increasing lnK variance due to enhanced channeling. Transverse displacement is a nonnormal for all s Y 2 and control planes close to the injection area, but after xI Y = 20 was found to be nearly normal even for high s Y 2 . Travel time distribution deviates from the Fickian model for large lnK variance and exhibits increasing skewness and a power law tail for large lnK variance, the slope of which decreases for increasing distance from the source; no anomalous features are found. Second moment of advective transport is analyzed with respect to the covariance of two Lagrangian velocity variables: slowness and slope which are directly related to the travel time and transverse displacement variance, which are subsequently related to the longitudinal and transverse dispersion. We provide simple estimators for the Eulerian velocity variance, travel time variance, slowness, and longitudinal dispersivity as a practical contribution of this analysis. Both two-parameter models considered (the advection-dispersion equation and the lognormal model) provide relatively poor representations of the initial part of the travel time probability density function in highly heterogeneous porous media. We identify the need for further theoretical and experimental scrutiny of early arrival times, and the need for computing higher-order moments for a more accurate characterization of the travel time probability density function. A brief discussion is presented on the challenges and extensions for which AFMCM is suggested as a suitable approach.Citation: Gotovac, H., V. Cvetkovic, and R. Andricevic (2009), Flow and travel time statistics in highly heterogeneous porous media, Water Resour. Res., 45, W07402,

The general formulation of the environmental risk problem captures the entire process of identifying the source term of the risk agent, its fate and transport through porous media, estimation of human exposure, and conversion of such exposure into the risk level. The contaminant fate and transport is modeled using the solute flux formulation evaluated with its first two moments, which explicitly account for the spatial variability of the velocity field, sorption properties, and parametric uncertainty through the first‐order analysis. The risk level is quantified on the basis of carcinogenicity using the risk factor (which describes the risk per unit dose or unit intake) employed to the total doses for individuals potentially consuming radionuclide‐contaminated groundwater. As a result of the probabilistic formulation in the solute flux and uncertainty in the water intake and dose‐response functions, the total risk level is expressed as a distribution rather than a single estimate. The results indicate that the geologic heterogeneity and uncertainty in the sorption estimate are the two most important factors for the risk evaluation from the physical and chemical processes, while the mean risk factor is a crucial parameter in the risk formulation.

Abstract. As a justification for the geoelectric characterization of the hydraulic conductivity field, this paper shows theoretically and empirically that electrical and hydraulic (eh) conductivities of aquifers can be correlated. The correlation, demonstrated at the microscale by a published network model of eh transport, arises from the fact that both eh conductivities are a function of connected pore volumes and connected pore surface areas. By considering skewed pore size distributions the microscale equations of eh conductivity scale up to power laws of porosity and specific surface area similar to Archie's law and the Kozeny equation. Also, a third, apparently unreported Archie-type power law relating electrical conductivity to specific surface area and the cation exchange phenomenon is predicted theoretically and confirmed experimentally. These equations imply a simple log-log linear correlation between eh conductivities that is either positive or negative. The positive correlation corresponds to a pore-volume-dominated electrical flow environment and the negative correlation corresponds to a pore-surface-dominated electrical flow environment. These relationships are supported by many published laboratory and field investigations cited in the paper.

Abstract. A theoretical framework for solute flux through spatially nonstationary flows in porous media is presented. The flow nonstationarity may stem from medium nonstationarity (e.g., the presence of distinct geological layers, zones, or facies), finite domain boundaries, and/or fluid pumping and injecting. This work provides an approach for studying solute transport in multiscale media, where random heterogeneities exist at some small scale while deterministic geological structures and patterns can be prescribed at some larger scale. In such a flow field the solute flux depends on solute travel time and transverse displacement at a fixed control plane. The solute flux statistics (mean and variance) are derived using the Lagrangian framework and are expressed in terms of the probability density functions (PDFs) of the particle travel time and transverse displacement. These PDFs are given with the statistical moments derived based on nonstationary Eulerian velocity moments. The general approach is illustrated with some examples of conservative and reactive solute transport in stationary and nonstationary flow fields. It is found based on these examples that medium nonstationarities (or multiscale structures and heterogeneities) have a strong impact on predicting solute flux across a control plane and on the corresponding prediction uncertainty. In particular, the behavior of solute flux moments strongly depends on the configuration of nonstationary medium features and the source dimension and location. The developed nonstationary approach may result in non-Gaussian (multiple modal) yet realistic behaviors for solute flux moments in the presence of flow nonstationarities, while these non-Gaussian behaviors may not be reproduced with a traditional stationary approach. IntroductionPredicting the migration of contaminants in subsurface flows is a major conceptual and practical challenge. The subsurface flow consists of tortuous and unpredictable flow pathways that result from natural geologic heterogeneity. As a consequence, the contaminant concentration is a random field that can be described only in the statistical sense. Since geologic media are heterogeneous and the medium heterogeneity generally cannot be described deterministically, it becomes quite common to treat medium properties as spatial random variables. That is, they are unpredictable deterministically and have to be described in statistical terms. In turn, subsurface flow and transport are treated as stochastic processes. Most efforts in studying subsurface contaminant transport in random porous media have been focused on quantifying the expected concentration and the associated uncertainty

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