Pore-scale investigation of flow in saturated and unsaturated media: computational tools and upscaling

The flow in porous media is commonly described by averaged equations that are widely used in many practical applications. However the interest on a more detailed description of the flow at the pore-scale is increasing in the recent years. This is due mainly to the lack of knowledge and to the variability of macro-scale parameters and models that cause high uncertainty on the final quantity of interests. This is the case, for example, of the dispersion and reaction of particles and contaminants in groundwater, where the estimation of parameters and transport properties can vary by order of magnitudes. Another important example is the recent problem related to carbon storage and sequestration. To address these problems, two main directions can be undertaken: on one side there is a growing effort in developing uncertainty quantification tools based on stochastic partial differential equations that express explicitly the lack of knowledge and variability of parameter with random variables and random fields. On the other hand, all the sources of uncertainty must be better investigated to understand their physical basis and stochastic representation. Within this framework, in this work, we focus on the intrinsic variability of macro-scale flow and transport parameters coming from the inner pore-scale structure. Different methods for reconstructing binary heterogeneous materials are investigated and tested [1-3]. A set of realization of random porous media are generated and studied in terms of physical and transport properties (porosity, tortuosity, permeability, dispersivity) by solving the flow equations in the void space. The three-dimensional flow results are then averaged and used to assess the validity of simplified macro-scale models and to estimate the value and the overall variability of macro-scale parameters. These results can be used to understand more clearly the dependence of the parameters on the flow regime and porous medium properties and to give prior information to the stochastic description of the flow.