Evaluating transport in irregular pore networks

TL;DR

This paper introduces a versatile analytical framework combining an anisotropic Effective Medium Approximation with a continuum model to analyze transport in irregular porous media efficiently.

Contribution

It develops a generalized EMA that accounts for microscopic and macroscopic heterogeneity, enabling analytical transport equations for complex pore networks.

Findings

The model accurately predicts transport in irregular pore networks.

It handles microscopic connectivity variations effectively.

Comparison shows good agreement with numerical simulations.

Abstract

A general approach for investigating transport phenomena in porous media is presented. This approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort. The overall method combines a generalized Effective Medium Approximation (EMA) with a macroscopic continuum model in order to derive a transport equation with explicit analytical expressions for the transport coefficients. The proposed form of the EMA is an anisotropic and heterogeneous extension of Kirkpatrick's EMA [Rev. Mod. Phys. 45, 574 (1973)] which allows the overall model to account for microscopic alterations in connectivity (with the locations of the pores and the orientation and length of the throat) as well as macroscopic variations in transport properties. A comparison to numerical results for randomly generated networks with different properties is given, indicating the potential for this methodology to handle cases that would pose significant difficulties to many other analytical models