Random Walk Methods for Modeling Hydrodynamic Transport in Porous and Fractured Media from Pore to Reservoir Scale

Random walk (RW) methods are recurring Monte Carlo methods used to model convective and diffusive transport in complex heterogeneous media. Many applications can be found, including fluid mechanic, hydrology and chemical reactors modeling. These methods are easy to implement, very versatile and flexible enough to become appealing for many applications because they generally overlook or deeply simplify the building of explicit complex meshes required by deterministic methods. RW provides a good physical understanding of the interactions between the space scales of heterogeneities and the transport phenomena under consideration. In addition, they can result in efficient upscaling methods, especially in the context of flow and transport in fractured media. In the present study, we review the applications of RW to several situations that cope with diverse spatial scales and different insights into upscaling problems. The advantages and downsides of RW are also discussed, thus providing a few avenues for further works and applications.