Estimation of relative permeability curves in fractured media by coupling pore network modelling and volume of fluid methods

The relative permeability of porous and fractured media is an important concept for various technological applications including hydrocarbon recovery, CO2 sequestration, hydrogen storage, hydrology, and microfluidics. In pore-scale simulations, relative permeability curves can be obtained either by pore-network modelling or direct numerical simulations (e.g., Navier-Stokes based and Lattice Boltzmann methods). While pore network models rely on several conceptual mathematical and geometric simplifications compared to more rigorous direct numerical methods, pore network modelling is often the only option to conduct the fast numerical simulation at a core-scale and regular desktop PC within a reasonable time frame. In this study, we analyse the ability of the developed hybrid pore network modelling and volume of fluid methods (VOF-PNM) model to accurately predict the two-phase flow displacement in a ramified system of fractures. This is done by conducting a number of 2D and 3D two-phase flow simulations with different viscosity ratios, contact angles, and capillary numbers. The VOF-PNM output with respect to history-matched relative permeability and capillary pressure curves is then compared to the reference conventional VOF simulations using a range of validation metrics. Such benchmarking allows concluding that the developed VOF-PNM solver can model flow through a system of fractures with an acceptable accuracy compared to the widely used VOF method. In turn, the conventional dynamic PNM algorithm failed to match the relative permeability and capillary pressure when compared to the reference VOF simulations. In terms of computational time, the non-parallelised hybrid VOF-PNM model is at least two orders of magnitude faster than parallelised VOF simulation and only one order of magnitude slower than the conventional dynamic PNM algorithm. The findings are beneficial for simulating two-phase flow through a fractured system at a core scale, as a design tool for microfluidic devices, and for further evolution of the VOF-PNM model into a comprehensive tool for transient multi-scale multi-physics simulations in coal.