Porous media comprise a large range of natural or industrial materials with a broad spectrum of applications. It is part of our everyday life e.g. in form of bread, a simple rinsing sponge or a brick used for building. Thus, it has always been part of our environment.
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.