# A Dynamic Network Simulator for Immiscible Two-Phase Flow in Porous Media

## TL;DR

This paper introduces a comprehensive dynamic pore-network model with algorithms capable of simulating various two-phase flow patterns in porous media, capturing both transient and steady-state behaviors with different boundary conditions.

## Contribution

The paper develops a general set of algorithms for dynamic pore-network modeling of two-phase flow, capable of reproducing complex flow patterns and rheological transitions in porous media.

## Key findings

- Reproduces viscous, capillary fingering, and stable displacement patterns.
- Verifies the transition from linear to non-linear rheological behavior.
- Satisfies relations between seepage velocities in steady-state flow.

## Abstract

We present in detail a set of algorithms to carry out fluid displacements in a dynamic pore-network model of immiscible two-phase flow in porous media. The algorithms are general and applicable to regular and irregular pore networks in two and three dimensions with different boundary conditions. Implementing these sets of algorithms, we describe a dynamic pore-network model and reproduce some of the fundamental properties of both the transient and steady-state two-phase flow. During drainage displacements, we show that the model can reproduce the flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by altering the capillary number and the viscosity ratio. In steady-state flow, the model verifies the linear to non-linear transition of the effective rheological properties and satisfy the relations between the seepage velocities of two-phase flow in porous media.