Application of percolation, critical-path, and effective-medium theories for calculation of two-phase relative...

There has been active development of numerical pore-network simulation of two-phase immiscible flows in porous media in recent years. These models allow for generation of capillary pressure and relative permeability curves. However, percolation models provide an efficient alternative, with reduced reliance on numerical techniques. Implementation of effective medium or critical path theory along with the percolation model allows for evaluation of the relative permeability curves. Both approximations failed to match the irreducible water saturation for water relative permeability. While the effective medium approximation poorly matches the pore network simulator, the critical path approximation is shown to match the result of the oil relative permeability. Despite the difference in end points, there is qualitative agreement between critical path approximation and the pore network simulator. Moreover, observed differences are not necessarily a drawback due to important boundary effects as discussed in the paper. Our results indicate that percolation-theory based predictions have the potential to become an efficient tool for upscaling by computing two-phase flow properties for numerous porosity subdomains.