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The control of drilling parameters, such as fluid pressure, mud weight, salt concentration, etc., is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, which is fundamental for deep oil drilling and hydraulic fracturing for gas extraction (“fracking”), a non-linear model of mechanical and chemo-poroelastic interactions among fluids, solutes and the solid matrix is discussed here. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid-saturated porous rock. If the non-linear term in these equations is larger than the diffusive term the solutions are quick, non-linear Burgers solitary waves, which are potentially destructive for deep operations. In our study the role of diffusion in presence of these solitary waves has been also analyzed. Then, following Civan (1998), both diffusive and shock waves are applied to fine particle …