Journal ArticleDOI
Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions
Abhijit Chaudhuri,Muddu Sekhar +1 more
TLDR
In this article, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields.Abstract:
Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.read more
Citations
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Journal ArticleDOI
Entropy generation due to three-dimensional double-diffusive convection of power-law fluids in heterogeneous porous media
TL;DR: In this paper, a numerical study of entropy generation due to double-diffusive natural convection in a 3D heterogeneous porous cubic saturated with power-law fluids and submitted to horizontal thermal and concentration gradients is presented.
Journal ArticleDOI
Predicting DNAPL mass discharge and contaminated site longevity probabilities: Conceptual model and high-resolution stochastic simulation
J. Koch,Wolfgang Nowak +1 more
TL;DR: In this paper, the authors proposed a physically and stochastically coherent model concept to simulate and predict crucial impact metrics for DNAPL contaminated sites, such as contaminant mass discharge and DNAPl source longevity.
Journal ArticleDOI
Constraining complex aquifer geometry with geophysics (2-D ERT and MRS measurements) for stochastic modelling of groundwater flow
Abhijit Chaudhuri,Muddu Sekhar,Marc Descloitres,Yves Goddéris,Laurent Ruiz,Laurent Ruiz,Jean-Jacques Braun,Jean-Jacques Braun +7 more
TL;DR: In this article, the authors assessed the potential of using geophysical surveys to describe the geometry of a hard rock-aquifer in a stochastic modelling framework and found that the spatial variability of the layer thickness had a significant effect on reducing the simulated effective steady seepage flux.
Journal ArticleDOI
Influence of the grain structure on solute transport in constructed inhomogeneous media from pore-scale simulations
TL;DR: In this paper, a finite element method (FEM) was adopted to simulate conservative solute transport in the porous media and the velocity field and plume evolution were analyzed, and the breakthrough curves (BTCs) and residence time distributions (RTDs) were calculated and the continuous time random walk (CTRW) inverse model was applied to fit the BTCs to reveal the influence of the grain structure on solutes transport quantitatively.
References
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Journal ArticleDOI
Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments
TL;DR: In this paper, the authors apply stochastic methods to the analysis and prediction of solute transport in heterogeneous saturated porous media and derive partial differential equations for three unconditional ensemble moments (the concentration mean, concentration covariance, and velocity concentration cross covariance) for a conservative solute.
Journal ArticleDOI
Probabilistic characterization of transport in heterogeneous media
TL;DR: In this article, the hydraulic properties of a random porous medium are modeled as spatial random processes and the concentrations over the whole domain are also random processes, with unknown probabilistic structure.
Journal ArticleDOI
Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 1. Theory and computational approach
TL;DR: Guadagnini and Neuman as mentioned in this paper developed complementary integrodifferential equations for second conditional moments of head and flux which serve as measures of predictive uncertainty; obtained recursive closure approximations for both the first and second conditional moment equations through expansion in powers of a small parameter σY which represents the standard estimation error of ln K(x).