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Multi-scale modeling and finite element simulation of diffusion in porous media
Doktorsavhandling, 2019

This thesis investigates transport processes in porous media on multiple scales by applying computational homogenization and finite element simulation. Biot’s equations

of (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.

Hydro-Mechanical Coupling

Fractured Rock

Poroelasticity

Three-Phase Concrete

Computational Homogenization

## Författare

### Nele Pollmann

Chalmers, Industri- och materialvetenskap, Material- och beräkningsmekanik

### N. Pollmann, R. Jänicke, J. Renner, H. Steeb; Numerical Investigation of the Effective Skempton Coefficient in Porous Rock Containing Fluid-Filled Fracture Networks

### N. Pollmann, R. Jänicke, J. Renner, H. Steeb; Experimental determination of the Skempton coefficient: Challenges and opportunities

### Diffuse interface modeling and variationally consistent homogenization of fluid transport in fractured porous media

European Journal of Mechanics, A/Solids,; Vol. 84(2020)

**Artikel i vetenskaplig tidskrift**

### N. Pollmann, F. Larsson, K. Runesson, K. Lundgren, K. Zandi, R. Jänicke; Modeling and computational homogenization of chloride diffusion in three-phase meso-scale concrete

Porous media are highly complex on different scales which gets clearer with the aid of an example such as sandstone. When hiking in the Elbe Sandstone Mountains one could take a closer look at the rock and get aware of small and large fractures as a form of

*heterogeneities*. Taking an even closer look, e.g. with a magnifier, small grains are visible such as in sand.

Of special interest is the behavior of this material if it is saturated with fluid (e.g. water, oil, gas). If the porous media is filled with fluid, transport processes occur, e.g in form of fluid flow. This is, among others, important for geothermal energy production, environmental remediation or the corrosion process of reinforced concrete buildings (due to de-icing fluid).

During the production of deep geothermal energy e.g., the rock is

*hydraulically stimulated*, i.e. fractures are induced by pumping water under high pressure in the ground. These fractures enhance the conductivity of the rock, which is used for energy production. The hydraulic stimulation of rock causes seismic attenuation, i.e. small to large earthquakes in the reservoir. Therefore, the ability to detect, to understand and to simulate seismic attenuation helps decision makers to forecast whether or not a rock region is suitable for hydraulic stimulation.

This thesis numerical examines the processes in porous media, to gain results that can e.g. be used to interpret field data such as of seismic exploration. Therefore different numerical approaches are investigated on the basis of the

*Theory of Porous Media*and validated against suitable benchmarks. In summary the thesis provides a deeper understanding of diffusion processes in porous media and investigates a suitable toolbox to compute the overall material behavior of porous media, taking into account heterogeneities such as fractures in rock or aggregate content in concrete, on different scales.

### Ämneskategorier

Maskinteknik

### Styrkeområden

Building Futures (2010-2018)

### ISBN

978-91-7905-170-9

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4637

### Utgivare

Chalmers tekniska högskola

VDL, Tvärgata 4C, Chalmers

Opponent: Professor Marc-André Keip, Institute of Applied Mechanics (CE), University of Stuttgart, Germany