  We develop and validate a new model to study simultaneous erosion and
deposition in three-dimensional porous media. We study the changes of the
porous structure induced by the deposition and erosion of matter on the solid
surface and find that when both processes are active, channelization in the
porous structure always occurs. The channels can be stable or only temporary
depending mainly on the driving mechanism. Whereas a fluid driven by a constant
pressure drop in general does not form steady channels, imposing a constant
flux always produces stable channels within the porous structure. Furthermore
we investigate how changes of the local deposition and erosion properties
affect the final state of the porous structure, finding that the larger the
range of wall shear stress for which there is neither erosion nor deposition,
the more steady channels are formed in the structure.
