InterPore2026

Investigation of a Velocity PDF-based Model for Dispersion in Porous Media

19 May 2026, 14:20

15m

Oral Presentation (MS09) Pore-Scale Physics and Modeling MS09

Speaker

Yilkut Aydin (Technical University of Munich)

Description

This study investigates a velocity PDF-based stochastic model for predicting particle dispersion in flow through porous media. Modeling dispersion involves an inherent trade-off: Pore-resolved simulations provide high resolution and accuracy but require substantial computational effort, whereas reduced-order models improve efficiency at the cost of physical detail. The model investigated here occupies a niche between these approaches, where a reduced-order description is enhanced through statistical upscaling from pore-resolved flow fields.
The model, initially developed by Meyer and Tchelepi [1] and further modified by Khooshapur [2], predicts particle dispersion by upscaling velocity statistics extracted from pore-resolved Eulerian flow fields. The underlying flow simulations and reference particle tracking data are time-dependent and three-dimensional, and obtained from direct numerical simulations (DNS) in explicitly resolved sphere-pack geometries [3,4]. The stochastic transport model itself is formulated in one dimension and targets longitudinal dispersion; transverse dispersion is therefore not addressed and is deferred to future work. The model is based on a generalized random walk framework, in which the Langevin equation for a massless point particle is augmented by stochastic dynamics in velocity space. The drift and diffusion coefficients governing the velocity-space evolution are determined directly from pore-scale velocity statistics.
The model is evaluated across a range of Peclet numbers, pore geometries, and flow regimes. Validation is performed against high-resolution Lagrangian particle tracking simulations using pore-resolved DNS data generated with the in-house, open-source flow solver MGLET [5,6,7], which serves as ground truth for assessing the upscaled dispersion predictions. The model’s ability to predict both the effective longitudinal diffusivity in the Gaussian asymptotic limit and the pre-asymptotic, time-dependent dispersion behavior is assessed within the scope of this study.
Across the explored parameter space, the model consistently reproduces the qualitative evolution of dispersion, including the transition from early-time non-Fickian behavior to late-time Fickian transport, as well as the transition between dispersion-dominated and diffusion-dominated transport along the Peclet number range. Quantitatively, the relative error in effective longitudinal diffusivity spans approximately 5% to 90% over the considered Peclet number range, with a mean error of about 50%, reflecting the strong sensitivity of dispersion to flow regime and Peclet number. One source of discrepancy is identified at low Peclet numbers, where transport approaches the pure diffusion limit and pore-scale geometric constraints induce hindered effective diffusivity, which is an effect not incorporated in the present model formulation. Similarly, while pre-asymptotic dispersion trends are captured qualitatively, exact quantitative agreement is not yet achieved at the time of writing.
Despite these limitations, the model offers substantial computational savings compared to fully resolved particle tracking in three-dimensional DNS, particularly in highly non-linear and turbulent flow regimes. As a stochastic upscaling approach grounded in pore-scale physics, the model provides a framework for estimating macroscopic dispersion while retaining sensitivity to flow heterogeneity. These results highlight both the potential and current limitations of velocity PDF–based models for pore-scale transport, with relevance to applications such as contaminant migration in groundwater, subsurface energy systems, and reactive mixing in porous materials.