Dynamic pore-network modeling (PNM) has been widely used to model two-phase flow in porous media. The IMPES-type (implicit-pressure explicit-saturation) algorithms that are commonly used for PNM are only numerically stable for a limited range of flow regimes—characterized by the capillary number Ca and fluid viscosity ratio M (the ratio between viscosity of the injected fluid and that of the displaced fluid). The limitations of the IMPES-type method include: 1) failure to converge for flow regimes that involve low Ca and/or unfavorable displacement (i.e., M<1); 2) mass conservation issues that become progressively worse for unfavorable displacements. We propose a novel fully-implicit framework to address these limitations. Our algorithm solves pressure and saturation simultaneously within each time step using Newton iterations—overcoming instability issues that arise in the IMPES-type algorithms due to weak coupling between pressure and saturation. A series of numerical experiments are performed which show that the new algorithm provides robust solutions for a wide range of flow regimes including near quasi-static flow (Ca is close to 0) and an M that spans 0.01~10. Exact mass conservation is observed for all simulations. The new fully-implicit dynamic PNM method provides a robust framework to study complex two-phase flow and transport problems at the pore scale.
