Uncertainty and sensitivity analysis of filtration models for non-Fickian transport and hyperexponential deposition

Abstract

Uncertainty and sensitivity analyses are carried out to investigate the predictive accuracy of the filtration models for describing non-Fickian transport and hyperexponential deposition. Five different modeling approaches, involving the elliptic equation with different types of distributed filtration coefficients and the CTRW equation expressed in Laplace space, are selected to simulate eight experiments. These experiments involve both porous media and colloid–medium interactions of different heterogeneity degrees. The uncertainty of elliptic equation predictions with distributed filtration coefficients is larger than that with a single filtration coefficient. The uncertainties of model predictions from the elliptic equation and CTRW equation in Laplace space are minimal for solute transport. Higher uncertainties of parameter estimation and model outputs are observed in the cases with the porous media and the colloid–medium interactions of higher heterogeneity. The parameters for the distribution of filtration coefficients could not be uniquely identified due to strong correlations. In the cases of heterogeneous colloid–medium interactions where hyper-exponential deposition is observed, the distribution of filtration coefficients could not be accurately determined by the effluent concentration profile alone. Measurements of deposition are necessary. The effluent concentrations around the breakthrough and around the end of colloid injection are more sensitive to dispersion coefficients than filtration coefficients, while deposition is more sensitive to filtration coefficients. Based on the insights and information provided by the uncertainty and sensitivity analysis of the filtration models, the following are concluded: (i) it is possible to improve the parameter estimation accuracy by doing more measurements at sensitivity-focused moments. (ii) the elliptic equation with distributed filtration coefficients is more accurate at modelling colloids filtration where heterogeneity of particle-medium interactions is dominant, and (iii) Both the elliptic equation and the CTRW equation are accurate at modeling transport in ground water or other systems where the median heterogeneity is dominant.