Modeling of two-phase porous flow with damage

Two-phase dynamics has been broadly studied in Earth Science in a convective system. We investigate the basic physics of compaction with damage theory and present preliminary results of both steady state and time-dependent transport when melt migrates through porous medium. In our simple 1-D model, damage would play an important role when we consider the ascent of melt-rich mixture at constant velocity. Melt segregation becomes more difficult so that porosity is larger than that in simple compaction in the steady-state compaction profile. Scaling analysis for compaction equation is performed to predict the behavior of melt segregation with damage. The time-dependent of the compacting system is investigated by looking at solitary wave solutions to the two-phase model. We assume that the additional melt is injected to the fracture material through a single pulse with determined shape and velocity. The existence of damage allows the pulse to keep moving further than that in simple compaction. Therefore more melt could be injected to the two-phase mixture and future application such as carbon dioxide injection is proposed.