A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

TL;DR

This paper introduces a Monte Carlo algorithm for simulating immiscible two-phase flow in porous media, offering computational efficiency improvements over traditional methods by leveraging configuration probabilities.

Contribution

The paper develops a novel Monte Carlo method based on configuration probabilities for steady-state two-phase flow in porous media, reducing computational complexity.

Findings

Monte Carlo time scales as the square of system size

Configuration probability is proportional to inverse flow rate

Algorithm offers potential computational advantages

Abstract

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.