We propose that there are two classes of temporal development in the degradation 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 permeability much as they develop. When these stripes are allowed to develop, they coalesce and worm holes form. We discuss how imposing different flow conditions such as constant flow and constant pressure influence the deposition process. Our conclusion is that constant pressure conditions typically lead to a slower permeability degradation compared to constant flow conditions as a direct consequence of the formation of low-permeability bands. We test our ideas by numerical simulations on a simple model for fines migration and deposition in porous media.