Diffusion of fluids in porous media with memory

In some geothermal areas the fluids may precipitate minerals in the pores of the medium, thus diminishing their size. To study the flow of these fluids we modify the law of Darcy by introducing a memory formalism represented by a derivative of fractional order simulating the effect of a decrease of the permeability in time. The diffusion in these media is studied, giving the distribution of the pressure of the fluid in a half space when the fluid pressure, at the plane bounding the half space, is constant or sinusoidal or in the form of a box in the time domain. The velocity of propagation of the phase allows us to model the flow in several cases of practical interest. A method is suggested to retrieve the two parameters defining the diffusion; a numerical test of the method gives encouraging results. (C) 1999 CNR. Published by Elsevier Science Ltd.