Behavior of viscoplastic rocks near fractures: mathematical modelling

Starting from conservation laws and basic thermodynamic principles, we derive equations for a two-phase granular fluid. The first phase is the granular viscoplastic Bingham fluid and the second phase is the viscous Newtonian fluid. We perform an asymptotic analysis of the equations for the flows in the Hele-Show cell when the channel width is well much below its length. While calculating the fluid fluxes-pressure gradient relationship, we derive laws of flow of the two-phase granular viscoplastic fluid through porous media. A criterium is formulated for the start up of the granular phase flow through a porous medium. Given a yield stress, we prove that such a phase does not flow if either or both pressure gradient and channel width are small. We calculated phase flows varying phase viscosities, phase resistivities and yield stress. We reveal reasons which slow down particle intrusion into a porous medium.