Transport Dynamics in Heterogeneous Porous Media

Transport dynamics in heterogeneous porous media encompass the movement and interaction of fluids and solutes through complex pore networks whose properties vary spatially across scales. At the pore‐scale, flow pathways, surface roughness and mineral heterogeneity govern local mixing and reaction rates, while at the Darcy‐scale these microscale processes are represented by averaged parameters such as hydraulic conductivity and dispersivity. Key transport mechanisms include advection by bulk flow, dispersion arising from velocity fluctuations, diffusion enhanced by pore geometry and chemical reactions that may alter local flow paths or solute speciation. Heterogeneity gives rise to non‐Fickian behaviour, long‐tail breakthrough curves and preferential channels that can accelerate or retard contaminant migration. Accurately predicting solute fate demands methods to upscale pore‐scale insights into continuum models, to characterise uncertainty in parameter fields and to quantify mixing‐limited reactions. These challenges are of global significance for groundwater management, carbon sequestration, contaminant remediation and resource recovery, where predictive fidelity underpins risk assessment and engineering design. Recent advances highlight the interplay between modelling frameworks—such as stochastic approaches, lamellar mixing theories and multi-rate mass transfer formulations—and experimental characterisation, reinforcing the need for integrated multi-scale strategies.

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Technical terms

Advection-Dispersion Equation: A continuum model combining bulk flow (advection) with spreading due to velocity heterogeneity (dispersion).

Darcy-scale: The macroscopic scale at which porous media are treated as a continuum and flow is governed by averaged properties.

Pore-scale: The microscopic scale of individual pores and grains where local flow velocities, mixing and reactions occur.

Péclet number: A dimensionless ratio of advective transport rate to diffusive transport rate, indicating the dominant transport mechanism.

Lamellar mixing: A conceptual framework describing the stretching and folding of concentration interfaces that enhances mixing in heterogeneous flows.

Stochastic calibration: A probabilistic approach to parameter estimation that accounts for uncertainty in spatially variable properties.

References

1. Upscaling the reaction rates in porous media from pore- to Darcy-scale. Chemical Engineering Journal (2024).
2. A numerical investigation of the effects of model parameterization on the delineation of source protection zones under uncertainty. Water Research (2024).
3. Signature of Non-Fickian Solute Transport in Complex Heterogeneous Porous Media. Physical Review Letters (2011).
4. Mixing in Porous Media: Concepts and Approaches Across Scales. Transport in Porous Media (2022).
5. A general real-time formulation for multi-rate mass transfer problems. Hydrology and Earth System Sciences (2009).