We propose that there are two classes of temporal development in the d
egradation of permeability of porous media due to deposition of fines:
(1) Deposition, and therefore permeability degradation, is localized
to bands growing orthogonally to the average local flow direction, and
(2) permeability degradation occurs in stripes parallel to the local
flow direction. These latter stripes do not influence total permeabili
ty much as they develop. When these stripes are allowed to develop, th
ey coalesce and worm holes form. We discuss how imposing different flo
w conditions such as constant flow and constant pressure influence the
deposition process. Our conclusion is that constant pressure conditio
ns typically lead to a slower permeability degradation compared to con
stant flow conditions as a direct consequence of the formation of low-
permeability bands. We test our ideas by numerical simulations on a si
mple model for fines migration and deposition in porous media.