TRANSMISSION CONDITIONS FOR FLOW THROUGH POROUS MEDIA WITH FRACTAL MICROSTRUCTURE

What is it about?

This work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously analyzed. Also, numerical experiments for each of them are presented to verify the theoretically predicted behavior of the phenomenon and some probabilistic versions are explored numerically to gain further insight on the phenomenon.

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Why is it important?

It is known that porous media has fractal structure. However, there has not been a mathematically rigorous treatment of the fluid exchange conditions between the rock matrix and pores, accounting for the fractal nature of the medium. Mathematical studies of the phenomenon, assuming periodicity or homogenization of the medium have been conducted, however, this is the first of its kind discussing the impact of the fractal structure.