Multiscale Dynamics in Micro-porous Fractured Systems: Theory and Experiments

Abstract:

Soils and rock systems exhibit surfaces with complex micro-scale topological features. Understanding flow and solute transport over micro-patterned surfaces is essential to improve our predictive understanding of transport in structurally heterogeneous porous media, which provides insight of many environmental processes including CO$_2$ sequestration and bioremediation. We are interested in seeking the relationship between surface topological structure and its impact on solute transport. We consider a thin fracture embedded in a permeable porous matrix. By means of homogenization technique, we upscale the transport equation and obtain a macro-scale dispersion coefficient which depends on the geometrical characteristic of the matrix, i.e. porous layer permeability and width. This expression generalizes a number of former studies, including the classical form of the Aris-Taylor dispersion coefficient and more recent results based on the assumption of purely diffusive mass transport in the matrix. Based on the upscaled equation, we provide a two-dimensional solution for the concentration profiles both inside the fracture and the matrix. Finally, we show good agreement between our theoretical predictions and the experimental data performed on a series of microfluidic cells with different matrix geometries/permeabilities for a wide range of Peclet numbers.