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. More experimental measurements at these moments are suggested to determine dispersion coefficients more accurately. More measurements of the steady-state effluent concentration or deposition are suggested to determine filtration coefficients more accurately.
- Deep bed filtration
- Median heterogeneity
- Particle heterogeneity
- Uncertainty and sensitivity analysis
- Elliptic equation