Stochastic analysis of transient three-phase flow in heterogeneous porous media

The spatial distribution of residual light nonaqueous phase liquid (LNAPL) is an important factor in reactive solute transport modeling studies. There is great uncertainty associated with both the areal limits of LNAPL source zones and smaller scale variability within the areal limits. A statistical approach is proposed to construct a probabilistic model for the spatial distribution of residual NAPL and it is applied to a site characterized by ultraviolet-induced-cone-penetration testing (CPT-UVIF). The uncertainty in areal limits is explicitly addressed by a novel distance function (DF) approach. In modeling the smallscale variability within the areal limits, the CPT-UVIF data are used as primary source of information, while soil texture and distance to water table are treated as secondary data. Two widely used geostatistical techniques are applied for the data integration, namely sequential indicator simulation with locally varying means (SIS-LVM) and Bayesian updating (BU). A close match between the calibrated uncertainty band (UB) and the target probabilities shows the performance of the proposed DF technique in characterization of uncertainty in the areal limits. A crossvalidation study also shows that the integration of the secondary data sources substantially improves the prediction of contaminated and uncontaminated locations and that the SIS-LVM algorithm gives a more accurate prediction of residual NAPL contamination. The proposed DF approach is useful in modeling the areal limits of the nonstationary continuous or categorical random variables, and in providing a prior probability map for source zone sizes to be used in Monte Carlo simulations of contaminant transport or Monte Carlo type inverse modeling studies.

Section: Introductionsupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Probabilistic data integration for characterization of spatial distribution of residual LNAPL

Hosseini

Deutsch

Biggar

et al. 2009

“…Stochastic methods have been widely used in the fields of hydrology (Cantet et al 2011;Haan 1994;Lee and Yoo 2001), hydraulics (Chen et al 2009;Erik 2011;Kim et al 2004) and agriculture (Perreault et al 2000;Wu and Wang 1998;Young et al 2011). The nonlinear nature of dynamic pressure and dissipation rate is confirmed from Figs.…”

Section: Wall Shear Stressmentioning

confidence: 79%

Numerical and multivariate stochastic approaches to characterize flow in a constructed wetland basin

Wei

Plappally

Soboyejo

et al. 2011

Reduction in specific and viscous dissipation rate in surface waters by flow control and contaminant removal are the goals of constructed wetlands. A twodimensional simulation study on surface flow through a constructed wetland in Guilin, China is performed. The flow through the wetland is modeled and dynamically simulated by distinct case studies by varying both inlet width and inflow rate. Nonlinear increase in peak dynamic pressure and specific dissipation rates as a function of increasing inflow rate is reported for the different cases studied. The results of the numerical models confirm an increase in viscous dissipation, shear stress and dynamic pressure within the wetland with increase in inflow rate. These modeling results are used as inputs for performing a statistical data analysis. Further, a multivariate stochastic statistical framework has been proposed for the prediction of dissipation as a function of variables including inflow rate, inlet geometry and wall shear stress. Multivariate and variance analysis is performed to validate the appropriateness of the theoretical models proposed. Results provide simplified meaningful suggestions to constructed wetland design and related applications.

“…This necessitates describing the conductivity and other parameters as random fields that satisfy certain statistical correlations. Many models have been developed to evaluate the uncertainty of groundwater flow and solute transport, such as the conventional Monte Carlo simulation, moment-equation method (Zhang 2002), stochastic finite element method (Ghanem 1998;Xiu and Karniadakis 2002), KLME approach (Chen et al 2009;Shi et al 2009), and stochastic collocation method (Lin and Tartakovsky 2009). The blooming of stochastic methods provide various tools for uncertainty qualification.…”

Section: Introductionmentioning

confidence: 99%

Application of multiscale finite element method in the uncertainty qualification of large-scale groundwater flow

Shi

Yang

Zeng

2011

In this article, we discuss the application of multiscale finite element method (MsFEM) to groundwater flow in heterogeneous porous media. We investigate the ability of MsFEM in qualifying the flow uncertainty. Monte Carlo simulation is employed to implement the stochastic analysis, and MsFEM is used to avoid a full resolution to the spatial variable conductivity field. Large-scale flow with high variability is investigated by inspecting the single realization as well as the probability distribution functions of head and velocity. The numerical results show that the performance of MsFEM depends on the ratio between the correlation length and the coarse element size. An accurate prediction to the velocity requires a much lower ratio than the head. The MsFEM has different convergence rates for the head and the velocity, while the convergence rates do not deteriorate as the variance grows.