Pressure and temperature dynamics in fluid-saturated porous-permeable rocks

A nonlinear model of temperature and pressure waves in one-dimensional fluid-saturated porous-permeable rocks is discussed in order to investigate hydrogeological problems affecting hyperthermal areas. Nonlinear solutions, consisting in waves moving with constant velocity V, are analyzed. They behave as perturbations that increase with time till a critical value for vertical pressure gradient is reached, a gradient that is related to the time-asymptotic Darcy velocity. From the geological point of view, the effect of rock fracturing phenomena can be schematized by using some of the solutions of our model, if one postulates that our coefficients depend on the waves vertical pressure gradients. This allows to interpret measurement of the time-evolution of the Darcy velocity, as measured in a superficial position, as a way to reconstruct the porous rock reaction to the temperature-pressure jump carried by these nonlinear waves.