Journal ArticleDOI
Stochastic modeling of macrodispersion in heterogeneous porous media
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TLDR
In this article, a method for the prediction of dispersion processes of inert solutes occurring in heterogeneous porous media, where the velocity field is assumed to be a space random function, is presented.Abstract:
A method for the prediction of dispersion processes of inert solutes occurring in heterogeneous porous media, is presented. Its main features are as follows: (1) The velocity field is assumed to be a space random function. Its moments are expressed through the physical parameters of the log transmissivity and head random fields by linearizing the flow equation. The random velocity, being a linear function of the head and log transmissivity, which are assumed to be jointly multivariate normal (MVN), is thus also MVN. Its pdf is completely defined by its first two moments. (2) The statistics of the dispersion process are obtained by the particle-tracking method through Monte Carlo simulations which are based on Gaussian conditioning. The method is applied to the Borden natural gradient tracer test (Freyberg, 1986), showing favorable results.read more
Citations
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An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions
Dongxiao Zhang,Zhiming Lu +1 more
TL;DR: In this article, a higher-order solution of the means and variance of hydraulic head for saturated flow in randomly heterogeneous porous media was obtained by the combination of Karhunen-Loeve decomposition, polynomial expansion, and perturbation methods.
Journal ArticleDOI
Simulation of dispersion in heterogeneous porous formations: Statistics, first-order theories, convergence of computations
TL;DR: In this paper, the results of numerical analysis of dispersion of passive solutes in two-dimensional heterogeneous porous formations are discussed, and the results suggest that quite different rates of convergence with Monte Carlo runs hold for different spatial moments and that over 1000 realizations are required to stabilize second moments even for relatively mild heterogeneity (sigma(Y)2 < 1.6).
Journal ArticleDOI
Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations
Vladimir Cvetkovic,Gedeon Dagan +1 more
TL;DR: In this article, a Lagrangian framework is used for analysing reactive solute transport by a steady random velocity field, which is associated with flow through a heterogeneous porous formation, and the reaction considered is kinetically controlled sorption-desorption.
Journal ArticleDOI
Review of Ground‐Water Quality Monitoring Network Design
Hugo A. Loáiciga,Randall J. Charbeneau,Lorne G. Everett,Graham E. Fogg,Benjamin F. Hobbs,Shahrokh Rouhani +5 more
TL;DR: In this article, the selection of sampling sites and temporal sampling frequency to determine physical, chemical, and biological properties of ground water quality monitoring network design is defined as a selection of sample sites and sampling frequency.
Journal ArticleDOI
A quasi‐linear theory of non‐Fickian and Fickian subsurface dispersion: 1. Theoretical analysis with application to isotropic media
TL;DR: In this article, a quasi-linear theory is presented which accounts for nonlinearity caused by the deviation of plume "particles" from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities.
References
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Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors return to the possible solutions X t (ω) of the stochastic differential equation where W t is 1-dimensional "white noise" and where X t satisfies the integral equation in differential form.
Journal ArticleDOI
Three‐dimensional stochastic analysis of macrodispersion in aquifers
Lynn W. Gelhar,Carl L. Axness +1 more
TL;DR: In this article, the dispersive mixing resulting from complex flow in three-dimensionalally heterogeneous porous media is analyzed using stochastic continuum theory, which is consistent with controlled field experiments and Monte Carlo simulations.
Journal ArticleDOI
A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process
TL;DR: The Borden aquifer was examined in great detail by conducting permeability measurements on a series of cores taken along two cross sections, one along and the other transverse to the mean flow direction as discussed by the authors.
Journal ArticleDOI
A Stochastic-Conceptual Analysis of One-Dimensional Groundwater Flow in Nonuniform Homogeneous Media
TL;DR: In this paper, the effects of stochastic parameter distributions on predicted hydraulic heads are analyzed with the aid of a set of Monte Carlo solutions to the pertinent boundary value problems, and the results show that the standard deviations of the input hydrogeologic parameters, particularly σy and σc, are important index properties; changes in their values lead to different responses for even when the means μy, μc, and μn are fixed.