Local pore size correlations determine flow distributions in porous media

TL;DR

This paper presents an analytical model linking local pore size correlations to flow distribution in porous media, validated by simulations and experiments, revealing how microstructural disorder influences flow patterns.

Contribution

The study introduces a novel analytical model that predicts flow distributions based on local pore correlations, supported by numerical simulations and experimental validation.

Findings

Flow distributions transition from delta to Gaussian to exponential with increasing disorder.

Numerical simulations confirm the analytical model's predictions.

Experimental data supports the numerical and analytical results.

Abstract

The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from $\delta$-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.