Stochastic finite element modeling of unsaturated flow and solute transport in porous media

A stochastic perturbation-based finite element formulation for transient unsaturated flow and solute transport in porous media was developed, implemented and verified. The proposed methodology provides an efficient way to incorporate the small-scale variability of soil properties into large-scale models. A computer code was developed to obtain the finite element solutions for the stochastic flow and solute transport equations. Numerical simulations were performed in order to predict the mean pressure head and concentrations distributions and their respective variances at different times. Results from the stochastic analysis were compared to solutions from analytical, deterministic and Monte Carlo simulations, as well as experimental results. The stochastic approach, which includes the variability of the soil properties in the formulation, predicted a slower movement of the moisture front in the vertical direction and a faster movement in the horizontal direction. The stochastic and deterministic results were also compared to field-measured values. The results predicted by the stochastic finite element theory presented in this work are in excellent agreement with experimental values. The mean chemical concentration profiles were compared to Monte Carlo simulation results and were in good agreement. The advantage of the perturbation approach is that it is very computationally efficient when compared to the Monte Carlo method. The concentration profiles were also compared to deterministic results and an enhancement of the contaminant spreading in both directions was observed for the stochastic approach. Detailed soil data, especially the measurements of unsaturated hydraulic conductivity are required for simulating unsaturated flow and contaminant transport through soils using the stochastic perturbation-based finite element approach developed in this study. The numerical simulation results presented here show that the stochastic perturbation-based finite element approach is a very attractive alternative to deterministic and Monte Carlo approaches in terms of cost, efficiency and accuracy of the results