Fluid Meniscus Algorithms for Dynamic Pore-Network Modeling of Immiscible Two-Phase Flow in Porous Media

We present in detail a set of algorithms for a dynamic pore-network model of immiscible two-phase flow in porous media to carry out fluid displacements in pores. The algorithms are universal for regular and irregular pore networks in two or three dimensions and can be applied to simulate both drainage displacements and steady-state flow. They execute the mixing of incoming fluids at the network nodes, then distribute them to the outgoing links and perform the coalescence of bubbles. Implementing these algorithms in a dynamic pore-network model, we reproduce some of the fundamental results of transient and steady-state two-phase flow in porous media. For drainage displacements, we show that the model can reproduce the flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by varying the capillary number and viscosity ratio. For steady-state flow, we verify non-linear rheological properties and transition to linear Darcy behavior while increasing the flow rate. Finally we verify the relations between seepage velocities of two-phase flow in porous media considering both disordered regular networks and irregular networks reconstructed from real samples.

Automated summary

The study presents a set of algorithms for simulating dynamic pore-network model of immiscible two-phase flow in porous media, applicable for both drainage displacements and steady-state flow. The algorithms effectively reproduce fundamental results of transient and steady-state two-phase flow in porous media, showing the ability to replicate flow patterns like viscous fingering, capillary fingering, and stable displacement by adjusting capillary number and viscosity ratio. Additionally, the algorithms verify nonlinear rheological properties and the transition to linear Darcy behavior with increasing flow rate, as well as establish relationships between seepage velocities in two-phase flow in porous media with regular and irregular networks.