Having known that in a real field scenario, shale is characterized by its average dispersive fracturing, how will you correlate the differences in filtration and inhibition properties with shale (clay content and size) and with drilling fluids
Shales are anisotropic to the propagation of seismic waves, please look at the following Open Acess Research Article to see if it has some answers to your question, I guess it does not include dispersion, which is a hard issue to address:
James G. Berryman, Seismic waves in rocks with fluids and fractures, Geophysical Journal International, Volume 171, Issue 2, November 2007, Pages 954–974, https://doi.org/10.1111/j.1365-246X.2007.03563.x
The filtration and inhibition properties of shale can be characterized using capillary suction time test and be substituted with methylene blue test, specific surface area and particle size analysis for clay content characterization.
Reference: Article Capillary Suction Time Tests on Selected Clays and Shales