Diffusion of fluids in porous media with memory

In some geothermal areas the ~uids may precipitate minerals in the pores of the mediumthus diminishing their size[ To study the ~ow of these ~uids we modify the law of Darcy by introducing a memory formalism represented by a derivative of fractional order simulating the e}ect of a decrease of the permeability in time[ The di}usion in these media is studied\ giving the distribution of the pressure of the ~uid in a half space when the ~uid 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 ~ow in several cases of practical interest[Amethod is suggested to retrieve the two parameters de_ning the di}usion^ a numerical test of the method gives encouraging results[ 0888 CNR[ Published by Elsevier Science Ltd