A new formulation for pore-network modeling of two-phase flow

Pore network models of two-phase flow in porous media are widely used to investigate constitutive relationships between saturation and relative permeability as well as capillary pressure. However, results of many studies show a discrepancy between calculated relative permeability and corresponding measured values. Often, calculated values overestimate the measured values. An important feature of almost all pore network models is that the resistance to flow is assumed to come from pore throats only; i.e., the resistance of pore bodies to the flow is considered to be negligible compare to the resistance of pore throats. We contend that this simplification may considerably affect the results for relative permeability curves. In this study, we present a new formulation for pore network modeling of two-phase flow, which allows for the calculation of wetting phase fluxes in the edges of (partially) drained pores. In a quantitative investigation, we have shown the significance of this effect. The pore space is represented by cubic pore bodies and parallelepiped pore throats in a Multi-Directional Pore Network model. This model allows for a distribution of coordination numbers ranging between 1 and 26. This topological property, together with geometrical distributions of pore sizes, is used to mimic the microstructure of real porous media. In the presence of the nonwetting phase, the wetting fluid is considered to fill only spaces along edges of cubic pore bodies. We show that the resistance to the flow of the wetting phase within these filaments of fluids are comparable to the resistance to the wetting phase flow within pore throats. Resulting saturation-relative permeability relationships show very good agreement with measured curves. Explicit representation of wetting phase filaments and calculation of different fluxes within pore bodies may also lead to improved predictions of transport properties such as dispersivities and mass transfer coefficients.