| The basic equations used to study the fluid diffusion in porous media have
been set by Fick and Darcy in the mid of the XIXth century but some data on
the flow of fluids in rocks exhibit properties which may not be interpreted
with the classical theory of propagation of pressure and fluids in porous
media (Bell and Nur, 1978; Roeloffs, 1988).
Concerning the fluids and the flow, some fluids carry solid particles which
may obstruct some of the pores diminishing their size or even closing them,
some others may chemically and physically react with the medium enlarging
the pores; so permeability changes during time and the flow occurs as if the
medium had a memory.
In this paper we show with experimental data that the permeability of sand
layers may decrease due to rearrangement of the grains and consequent
compaction, as already shown qualitatively by Elias and Hajash (1992).
We also provide a memory model for diffusion of fluids in
porous media which fits well the flux rate observed in five laboratory
experiments of diffusion of water in sand. Finally we show that the flux
rate variations observed during the experiments are compatible with the
compaction of sand, due to the amount of fluid which went through the grains
locally, and therefore with the reduction of porosity. |