A Monte Carlo assessment of Eulerian flow and transport perturbation models

Hassan, Ahmed E.; Cushman, John H.; Delleur, J. W.

doi:10.1029/98wr00011

Cited by 82 publications

(57 citation statements)

References 81 publications

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“…provided ®rst-order analytical solutions for the longitudinal effective dispersion coef®cient, as well as for the expected value of the longitudinal spatial plume moment by assuming the log conductivity as a random space function of stationary increments characterized by a power law semivariogram. Hassan et al (1997Hassan et al ( , 1998 carried out Monte Carlo studies of¯ow and transport to study tracer migration in porous media with in®nite and ®nite integral scales. In their work, hydraulic conductivity was assumed to obey fBm statistics with in®nite integral scale or to have an exponential covariance structure with ®nite integral scale.…”

Section: Introductionmentioning

confidence: 99%

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

Zhu

2001

Stochastic Environmental Research and Risk Assessment

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A stochastic simulation is performed to study multiphase¯ow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (strati®cation) of fractal media on relative dispersivities is investigated and discussed. The results indicate the signi®cance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the in¯uence on the water phase is more signi®cant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most signi®cant increase against the plume scale.

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Section: Introductionmentioning

confidence: 99%

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

Zhu

2001

Stochastic Environmental Research and Risk Assessment

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“…The method for computing the first moments is similar to the numerical particle tracking method [Hassan et al, 1998]. From (25) and (29), τ τ and τ η can be obtained based on the calculated results of η η , u 1 η and u 2 η .…”

Section: Methods Of Moment For Groundwater Glow and Solute Transport Imentioning

confidence: 99%

On stochastic modeling of groundwater flow and solute transport in multi-scale heterogeneous formations

Hu¹,

Wu²,

He³

2004

Mat. apl. comput.

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Abstract.A numerical moment method (NMM) is applied to study groundwater flow and solute transport in a multiple-scale heterogeneous formation. The formation is composed of various materials and conductivity distribution within each material is heterogeneous. The distribution of materials in the study domain is characterized by an indicator function and the conductivity field within each material is assumed to be statistically stationary. Based on this assumption, a general expression is derived for the covariance function of the composite field in terms of the covariance of the indicator variables and the statistical properties of the composite materials. The NMM is used to investigate the effects of various uncertain parameters on flow and transport predictions in two case studies. It is shown from the study results that the two-scale stochastic processes of heterogeneity will both significantly influence the flow and transport predictions, especially for the variances of hydraulic head and solute fluxes. This study also shows that the NMM can be used to study flow and transport in complex subsurface environments. Therefore, the method may be applicable to complex environmental projects.Mathematical subject classification: 60H30, 60G60.

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“…The popular and simple Monte Carlo simulation method (MCSM) is based on generating a large number of equally likely random realizations for obtaining statistical moments of the dependent variable while using a numerical method (e.g. finite difference, finite element, finite volume) for solution of the deterministic system for each realization (Bellin et al 1992;Bosma et al 1995;Hassan et al 1999). This method is computationally exhaustive when a few thousands of realizations are required especially for a higher degree of medium heterogeneities along with higher space-time grid resolution.…”

Section: Introductionmentioning

confidence: 99%

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

Chaudhuri

Sekhar

2006

Stoch Environ Res Ris Assess

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During probabilistic analysis of flow and transport in porous media, the uncertainty due to spatial heterogeneity of governing parameters are often taken into account. The randomness in the source conditions also play a major role on the stochastic behavior in distribution of the dependent variable. The present paper is focused on studying the effect of both uncertainty in the governing system parameters as well as the input source conditions. Under such circumstances, a method is proposed which combines with stochastic finite element method (SFEM) and is illustrated for probabilistic analysis of concentration distribution in a 3-D heterogeneous porous media under the influence of random source condition. In the first step SFEM used for probabilistic solution due to spatial heterogeneity of governing parameters for a unit source pulse. Further, the results from the unit source pulse case have been used for the analysis of multiple pulse case using the numerical convolution when the source condition is a random process. The source condition is modeled as a discrete release of random amount of masses at fixed intervals of time. The mean and standard deviation of concentration is compared for the deterministic and the stochastic system scenarios as well as for different values of system parameters. The effect of uncertainty of source condition is also demonstrated in terms of mean and standard deviation of concentration at various locations in the domain.

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A Monte Carlo assessment of Eulerian flow and transport perturbation models

Cited by 82 publications

References 81 publications

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

On stochastic modeling of groundwater flow and solute transport in multi-scale heterogeneous formations

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

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