Analytical model for tracer dispersion in porous media

TL;DR

This paper introduces a new analytical model for tracer dispersion in laminar flow through porous media, accurately capturing behavior across a wide range of Peclet numbers without regime subdivision.

Contribution

It presents a novel analytical approach that describes dispersion behavior comprehensively and introduces the concept of a critical Peclet number linked to pore structure.

Findings

Model accurately describes dispersion over 8 orders of magnitude of Peclet numbers.

Identifies a new material property, the critical Peclet number, related to pore geometry.

Eliminates the need for empirical power laws or regime segmentation.

Abstract

In this work, we present a novel analytical model for tracer dispersion in laminar flow through porous media. Based on a straightforward physical argument, it describes the generic behavior of dispersion over a wide range of Peclet numbers (exceeding 8 orders of magnitude). In particular, the model accurately captures the intermediate scaling behavior of longitudinal dispersion, obviating the need to subdivide the dispersional behavior into a number of disjunct regimes or using empirical power law expressions. The analysis also reveals the existence of a new material property, the critical Peclet number, which reflects the mesoscale geometric properties of the microscopic pore structure.