  In the mathematical modelling of compactional flow in porous media, the
constitutive relation is typically modelled in terms of a nonlinear
relationship between effective pressure and porosity, and compaction is
essentially poroelastic. However, at depths deeper than 1 km where pressure is
high, compaction becomes more akin to a viscous one. Two mathematical models of
compaction in porous media are formulated and the noninear equations are then
solved numerically. The essential features of numerical profiles of poroelastic
and viscous compaction are thus compared with asymptotic solutions. Two
distinguished styles of density-driven compaction in fast and slow compacting
sediments are analysed and shown in this paper.
