Towards a Non-linear Theory for Induced Seismicity in Shales

We analyze the pore transmission of fluid pressure p and solute density ρ in porous rocks. To investigate shale deformation, fundamental for deep oil drilling and for gas extraction (“fracking”), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is discussed. The solutions of the model are quick non-linear Burger's solitary waves, potentially destructive for deep operations. Following Civan [2], diffusive and shock waves are applied to fine particles filtration. Then the delaying effects of fine particles filtration is compared with fractional model time delay and the fractional order parameter can be realistically estimate.