We present a dynamic network model for modeling two-phase flow. We account for wetting layer flow, meniscus oscillation, and the dynamics of snapoff. Interfaces are tracked through pore elements using a modified Poiseuille equation for the equivalent hydraulic resistance of the fluids between the pore element centers. The model is used to investigate the effects of capillary number and viscosity ratio on displacement patterns and fractional flow in primary drainage. We show that the amount of snapoff increases with increasing capillary number and decreasing wetting phase viscosity. For capillary numbers lower than approximately ${10}^{-5}$, the pore-scale fluid distribution and fractional flow are similar to those obtained using a quasistatic model that ignores viscous forces. The contribution of oil transport from ganglia, formed by snapoff, is negligible except for very large capillary numbers, greater than around $0.1$.

• Received 21 January 2004

DOI:https://doi.org/10.1103/PhysRevE.71.016308