Radek Fučík

Discontinous Galerkin and Mixed-Hybrid Finite Element Approach to Two-Phase Flow in Heterogeneous Porous Media with Different Capillary Pressures

Abstract A modern numerical scheme for simulation of flow of two immiscible and incompressible phases in inhomogeneous porous media is proposed. The method is based on a combination of the mixed-hybrid finite element (MHFE) and discontinuous Galerkin (DG) methods. The combined approach allows for accurate approximation of the flux at the boundary between neighboring finite elements, especially in heterogeneous media. In order to simulate the non-wetting phase pooling at material interfaces (i.e., the barrier effect), we extend the approach proposed in Hoteit and Firoozabadi (2008) by considering the extended capillary pressure condition. The applicability of the MHFEDG method is demonstrated on benchmark solutions and simulations of laboratory experiments of two-phase flow in highly heterogeneous porous media.

Effect of NAPL Source Morphology on Mass Transfer in the Vadose Zone

The generation of vapor-phase contaminant plumes within the vadose zone is of interest for contaminated site management. Therefore, it is important to understand vapor sources such as non-aqueous-phase liquids (NAPLs) and processes that govern their volatilization. The distribution of NAPL, gas, and water phases within a source zone is expected to influence the rate of volatilization. However, the effect of this distribution morphology on volatilization has not been thoroughly quantified. Because field quantification of NAPL volatilization is often infeasible, a controlled laboratory experiment was conducted in a two-dimensional tank (28 cm × 15.5 cm × 2.5 cm) with water-wet sandy media and an emplaced trichloroethylene (TCE) source. The source was emplaced in two configurations to represent morphologies encountered in field settings: (1) NAPL pools directly exposed to the air phase and (2) NAPLs trapped in water-saturated zones that were occluded from the air phase. Airflow was passed through the tank and effluent concentrations of TCE were quantified. Models were used to analyze results, which indicated that mass transfer from directly exposed NAPL was fast and controlled by advective-dispersive-diffusive transport in the gas phase. However, sources occluded by pore water showed strong rate limitations and slower effective mass transfer. This difference is explained by diffusional resistance within the aqueous phase. Results demonstrate that vapor generation rates from a NAPL source will be influenced by the soil water content distribution within the source. The implications of the NAPL morphology on volatilization in the context of a dynamic water table or climate are discussed.

An Efficient and Robust Numerical Solution of the Full-Order Multiscale Model of Lithium-Ion Battery

We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the finite difference discretization of the diffusion equations combined with an original iterative scheme for solving the integral formulation of the laws of electrochemical interactions. We demonstrate that our implementation is fast and stable over the expected lifetime of the cell. In contrast to some simplified models, it provides physically consistent results for a wide range of applied currents including high loads. The algorithm forms a solid basis for simulations of cells and battery packs in hybrid electric vehicles, with possible straightforward extensions by aging and heat effects.