โ Scribed by Michele Caputo
No coin nor oath required. For personal study only.
In some geothermal areas the ~uids may precipitate minerals in the pores of the medium\ thus 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[ A method is suggested to retrieve the two parameters de_ning the di}usion^a numerical test of the method gives encouraging results[ ร 0888 CNR[ Published by Elsevier Science Ltd[ Keywords] Porous media\ Memory\ Di}usion\ Darcy|s law[ Nomenclature A "m 1 s -0 # di}usivity รฐsee Eq[ "8#ล[ A"z# "m 1 s -0ยฆa # pseudodi}usivity รฐsee Eq[ "8#ล[ Dp -BDs kk :2 ratio of the rate of change of ~uid pressure Dp to that of the mean hydrostatic part of the stress tensor Ds kk "B is the so! called Skempton|s coe.cient#[ c "m 1 s -0 # di}usivity รฐsee Eq[ "7#ล[ G "kg s -1 m -0 # shear modulus of the medium[ m "kg# ~uid mass per unit volume of the medium[ m 9 "kg# ~uid mass per unit volume of the medium in the undisturbed condition[ p"x\t# "kg s -1 m -0 # ~uid pressure[
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