The onset of fluid invasion and flow development in a viscoplastic fluid

During cementing of oil and gas wells, sufficiently over-pressured fluids may enter from the surrounding rock into a gelled cement slurry. This fluid invasion may lead to failure of well integrity. For Newtonian fluids, once the pore pressure balances the hydrostatic pressure and any capillary effect, invasion occurs. In contrast, yield stress fluids may remain stationary under the same pore pressure. We investigate the critical amount of over-pressure which is sufficient to overcome a combination of static pressure, yield stress and interfacial tension available in this problem.