Non - linear concentration waves of pollutants in fluid - saturated porous rocks: constitutive equations approach and some examples of numerical solutions in the phase plane

The dynamics of fluid - saturated porous rock is a particularly interesting problem in geophysics and hydrology, nevertheless it is very important in environmental protection as well since it is able to describe, in a lot of situations, the propagation of pollutant substances dissolved in porous environmental matrices. It has been show that, for these systems, the nonlinear effects can be very important to consider. In this paper we'll discuss two novel approaches to the study of the above dynamics: one based on constitutive and conservation equations, the other considering the mass - balance equations for the solute flow and for adsorption rate of solute on the poroelastic matrix. We have shown the first model correctly describes the nonlinear behavior of the fluid pore pressure and pollutants concentration while the second gives the nonlinear term describing advection of which some numerical solutions has been calculated.