Lagrangian Statistics and Modeling of Pore-Scale Dispersion in Heterogeneous Natural Porous Media

Abstract:

Recent advances made in the area of micro-CT scanning of natural pore-space geometries enable detailed investigations of flow and transport processes at the pore-scale, e.g., [Bijeljic et al., Phys. Rev. E, 87, 2013]. A study is reported of Lagrangian statistics of fluid-particle velocity and acceleration in natural porous media of different rock type. The underlying 3d pore-space geometries were obtained by means of micro-CT scans of a beadpack, Bentheimer sandstone, and Ketton and Estaillades carbonates. Based on these statistics, we introduce a new Lagrangian model for transport that reproduces the aforementioned statistics. Our model is based on a spatio-temporal Markov process of the Lagrangian velocity of fluid particles, where the model parametrization is related to the medium characteristics. Transport predictions are validated against flow and transport results from pore-scale direct numerical simulation. The new model enables the detailed investigation of the transition between non-Fickian and Fickian dispersion in real porous media. Moreover, the model sheds light on the connection between geometrical pore-space characteristics and transport behavior.