# A framework for objectively comparing competing invasion percolation models based on highly-resolved image data

## TL;DR

This paper introduces a framework to compare invasion percolation models using high-resolution images, helping predict gas migration in porous media for applications like carbon storage.

## Contribution

A novel quantitative framework for comparing macroscopic IP models in transitional and continuous gas flow regimes using high-resolution experimental data.

## Key findings

- Some macroscopic IP models perform well in transitional and continuous gas flow regimes.
- Pore-scale heterogeneity significantly affects model performance.
- IP models can reduce computational costs compared to continuum-based models in certain applications.

## Abstract

Predicting gas migration in water-saturated porous media (a multiphase flow problem) is essential for applications such as carbon dioxide sequestration, hydrogen storage, and groundwater remediation. This process is challenging because gas migration can occur either as continuous or discontinuous flow, depending on the flow rate and the properties of the porous medium. Numerous variations of Invasion-Percolation (IP) models can simulate multiphase flow across different scales (from pore-scale to macroscopic), but the literature suggests that IP models are best suited for the discontinuous gas flow regime; other regimes have not been systematically evaluated. Here, we present a quantitative framework for comparing and ranking macroscopic IP models against high-resolution experimental data from transitional and continuous gas flow regimes. The analysis employs a diffused Jaccard coefficient to measure the similarity between model outputs and time-series two-dimensional images from gas injection experiments in water-saturated sand. To represent pore-scale heterogeneity, we run each model version on several random realizations of the initial invasion threshold field. The Jaccard coefficient was averaged over all realizations per model version to evaluate performance and calibrate model parameters. Depending on the application domain, some macroscopic IP model versions are suitable for these previously unexplored flow regimes. We also find that heterogeneity in the initial invasion threshold field strongly influences model performance. The observed applicability of IP models in these regimes can substantially reduce computational costs compared to continuum-based models for applications such as carbon dioxide storage and groundwater protection, although their ultimate use depends on the specific research question being addressed. The proposed comparison framework is not limited to gas–water systems in porous media but generalizes to any modelling situation accompanied by spatially and temporally resolved data.