Porous compaction in transient creep regime and implications for melt, petroleum, and CO2 circulation

Liquid segregation through a porous medium depends on the ability of the matrix to deform and compact. Earth's materials have a complex rheology, in which the balance between the elastic and viscous contribution to the deformation is time-dependent. In this paper, we propose a Burger-type model to investigate the implications of transient rheology for viscous compaction of a porous material. The model is characterized by three dimensionless parameters: (1) the Deborah number, De, defined as the ratio of an elastic timescale over the compaction timescale, (2) the ratio of the transient and steady viscosities, lambda(mu), and (3) the ratio of the transient and steady elastic moduli, lambda(G). For De < 10(-2) the compaction occurs in the classic viscous mode, and solitary waves (magmons) are generated. For larger De, compaction is mainly controlled by lambda(mu). For small transient viscosity, compaction occurs in an elastic mode, and shock waves are generated. For increasing lambda(mu), two new regimes are observed, first shaggy'' shock waves and then polytons''. Shaggy shock waves are characterized by the presence of secondary peaks at the wave propagation front. The length scale of the peaks is a decreasing function of lambda(G), and their amplitude decreases along the propagation. In the polytons regime, the peaks tend to detach and mimic the behavior of solitary waves. Polytons and shaggy shock waves are expected both in the mantle and in sedimentary basins. Polytons will require a particular attention as they imply larger extraction velocities and smaller compaction length scales than the usual magmons.