Coupling of pore network modelling and volume of fluid methods for multiphase flow in fractured media

Modelling multiphase flow in fractured media is a challenging multi-disciplinary problem which is of particular importance for the production of hydrocarbons from unconventional geological formations. At the pore-scale, this can be studied using pore network models that are computationally efficient due to the employment of pore-space geometrical simplifications. There are two distinctive approaches to pore network modelling: quasi-static and dynamic. However, only dynamic pore network models allow capturing the transient nature of the multiphase flow. Nevertheless, the dynamic models have a number of limitations including numerical oscillations and the inability of interface tracking in a particular network element. In order to overcome these drawbacks, a hybrid numerical method which combines the Hagen-Poiseuille analytical solution of the Navier-Stokes equations and the volume of fluid advection scheme is developed and validated. The proposed multiphase model is benchmarked against the conventional volume of fluid implementation for various drainage and imbibition cases using two-dimensional demo cases. Besides, three-dimensional simulations are also performed to ensure the applicability of the proposed model to real fractured media. The single pressure algorithm is employed while the capillary pressure drop is explicitly introduced as an additional term in the Hagen-Poiseuille equation. The conducted validation and following analysis show the applicability of the developed model for a wide range of Reynolds and capillary numbers and viscosity ratio. Thus, the new model can be used to investigate transient immiscible multiphase flow phenomena in fractures by pore network modelling.