Multi-scale modeling and finite element simulation of diffusion in porous media
Nele Pollmann · Chalmers Research (Chalmers University of Technology) · 2019
Porous media comprise a large range of natural and industrial materials and are typically complex on multiple length scales. At lower (micro-scopic) length scales, such media consist of a solid skeleton and fluid-filled pores in between. At higher (macro-scopic) length scales, transport of a migrating pore fluid can be observed in addition to the mechanical stress-strain response. The interaction between the pore fluid and the solid skeleton determines, in addition to the properties of the individual phases, the fully coupled response of the medium. Therefore, the investigation of macro-scale properties needs to take into account the processes between micro- and meso-scopic heterogeneities.This thesis investigates transport processes in porous media on multiple scales by applying computational homogenization and finite element simulation. Biot’s equationsof (linear) consolidation are introduced and combined with sharp and diffuse interface formulations that are established to investigate the effect of meso-scale heterogeneities, e.g. in form of fractures, on the overall material behavior. The scale transition of the heterogeneous porous meso-scale towards an homogeneous macro-scale problem is derived via Variationally Consistent Computational Homogenization.Taking into account this modeling framework, the thesis investigates:1) How the numerical modeling of heterogeneous porous media can be used to calibrate laboratory experiments.2) How the fluid transport in fractured rock can be modeled by applying sharp and diffuse interface formulations.3) How the effective diffusivity of porous media can be derived for the special case of three-phase concrete, where diffusion takes place preferably on interfaces in the structure. In this industrial porous material, fluid transport is not a relevant process but rather the diffusion of chloride ions in the fluid phase is of interest.All in all, the thesis reveals limits and establishes possibilities by the numerical modeling of heterogeneities in porous media with the aim to provide a deeper understanding of the transport processes in porous media on multiple scales.