Pore-network models and effective medium theory: A convergence analysis

TL;DR

This paper investigates the convergence between effective medium theory and pore-network models in predicting electrical conductance in porous media, analyzing how network size affects their agreement and limitations.

Contribution

It provides a detailed convergence analysis between effective medium theory and pore-network models, including power law models and limitations for thin media.

Findings

Convergence improves with increasing network size.

Effective medium theory matches pore-network results for large networks.

Limitations of effective medium theory are demonstrated in thin media.

Abstract

The convergence between effective medium theory and pore-network modelling is examined. Electrical conductance on two and three-dimensional cubic resistor networks is used as an example of transport through composite materials or porous media. Effective conductance values are calculated for the networks using effective medium theory and pore-network models. The convergence between these values is analyzed as a function of network size. Effective medium theory results are calculated analytically and numerically. Pore-network results are calculated numerically using Monte Carlo sampling. The reduced standard deviations of the Monte Carlo sampled pore-network results are examined as a function of network size. Finally, a "quasi-two-dimensional" network is investigated to demonstrate the limitations of effective medium theory when applied to thin porous media. Power law fits are made to these data to develop simple models governing convergence. These can be used as a guide for future research that uses both effective medium theory and pore-network models.