Water flow and solute mass flux in heterogeneous porous formations with spatially random porosity

Advances in Water Resources

2007

“…Using the Crank-Nicholson formulation for the first-order time derivative, the global FE equations (14) and (15) can be further simplified as…”

Section: Deterministic Fem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of biodegradation in a 3-D heterogeneous porous medium using nonlinear stochastic finite element method

Advances in Water Resources

2007

“…The random spatial variability in the physical and chemical properties of the porous medium during the transport of reactive solutes in a heterogeneous porous medium result in (1) an uncertainty in the distribution of concentration field [ Tang and Pinder , 1979; Dagan , 1989; Kapoor and Gelhar , 1994; Chaudhuri and Sekhar , 2005a] and (2) the field scale effective properties being quite different from the laboratory values [ Dagan , 1989; Gelhar , 1993; Hu et al , 1997; Huang and Hu , 2000; Hassan , 2001; Chaudhuri and Sekhar , 2005b]. Some of these studies have looked into the discrepancy between effective properties while modeling the system as heterogeneous medium instead of a homogeneous medium with uniform properties.…”

Section: Introductionmentioning

confidence: 99%

Stochastic finite element method for analysis of transport of nonlinearly sorbing solutes in three‐dimensional heterogeneous porous media

Water Resources Research

2007

[1] The probabilistic analysis by Monte Carlo simulation method (MCSM) for the transport of nonlinear reactive solutes in a three-dimensional heterogeneous porous medium is a computationally prohibitive task. For linear transport problems, the perturbation-based stochastic finite element method (SFEM) has been found to be computationally efficient with acceptable accuracy. This provides a motivation to develop the SFEM for the nonlinear reactive solute transport. In the present study, SFEM is developed for the transport of equilibrium nonlinear sorbing solutes, which follow the Langmuir-Freundlich isotherm. This method produces a second-order accurate mean and a first-order accurate standard deviation of concentration. In this study, the governing medium propertis viz. hydraulic conductivity, dispersivity, molecular diffusion, porosity, sorption, and decay coefficients are considered to vary randomly in space. The performance of SFEM is compared to MCSM for both one-and three-dimensional transport problems. The mean and the standard deviation of concentration for various test cases obtained with the SFEM compares well for the mild heterogeneity cases (standard deviation of log hydraulic conductivity less than 0.85) tested. SFEM produces a sharp front for the mean and the standard deviation of concentration while fronts obtained by MCSM are found to be dispersive. The error associated with the results obtained by SFEM is sensitive to the boundary conditions, the size of the domain, and the plume size. For a higher nonlinearity of sorption isotherm, the prediction uncertainty is higher. The pattern of the statistical moments of concentration is similar for cases with different correlation lengths of the parameters.

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“…In the last three decades, several studies have been made for analyzing probabilistic behavior of flow and transport in the groundwater system considering parameters such as hydraulic conductivity, porosity, sorption coefficient etc as random fields. The results of such probabilistic analysis in solute transport studies were mainly presented either in terms of effective properties which were derived from spatial or temporal plume moments (Dagan 1989;Gelhar 1993;Hu et al 1997;Huang and Hu 2000;Hassan 2001;Chaudhuri and Sekhar 2005a) or mean and standard deviation of concentration (Tang and Pinder 1979;Dagan 1989;Kapoor and Gelhar 1994).…”

Section: Introductionmentioning

confidence: 99%

Stochastic modeling of solute transport in 3-D heterogeneous porous media with random source condition

Stoch Environ Res Ris Assess

2006