Different regimes of compaction driven flow have been studied within the framework of a poro-viscoelastic medium. A single dimensionless parameter, the Deborah number De, has been identified, which enables the portrayal of the solution from the purely viscous matrix limit (De << 1) to the poro-elastic (De >> 1) matrix limit. In viscous limit the evolution of a porosity disturbance (porosity wave) is governed by nonlinear convection-diffusion equation, while in the poro-elastic limit it evolves according to a Burgers-like non-linear advection equation. In both regimes porosity waves of higher amplitude propagate faster. However in the viscous limit porosity waves go through each other in soliton-like fashion, while in poro-elastic limit they coalesce and thus enhance melt segregation. The introduction of other variables, such as chemistry, would induce different responses in the flow for low and high De, allowing for diverse feedback situations.