Research Article

Upscaling Transport and Sorption Processes via Spatial Markov Model in a Three-Dimensional Porous Domain

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Abstract

The simulation of transport phenomena in porous media poses computational challenges related to the inherent heterogeneity and complexity of natural porous structures. In this work, we introduce a numerical tool grounded on the particle tracking method and the trajectory-based spatial Markov model (tSMM) to model pore-scale transport, aswell as a dsorption and desorption processes. The tSMM is an upscaling approach that accounts for the correlation between consecutive particle trajectory paths over a fixed distance, which enables predicting transport across larger scales. The SMM demonstrates accurate prediction of diffusive and adsorptive/desorptive phenomena, benchmarking the results against the direct numerical simulation outcomes. The method is based on an iterative procedure where each step is characterized by relying on a sample of simulated trajectories. The analysis demonstrates that selecting consecutive trajectories based on the outlet-inlet position provides more accuracy compared to assigning a uniform weight to each trajectory. The optimal parameterization of tSMM exhibits variability with P´eclet numbers, underscoring a correlation between transport characteristics and the number of trajectories required for accurate predictions. Solute breakthrough at distinct locations reveals the impact of adsorptive Damköhler. Higher adsorptive Damköhler numbers lead to prolonged particle arrival times and distinctive arrival concentration patterns, that are closely matched by our low-cost upscaled approximation.

Keywords: Solute Transport, Adsorption, Porous Media, Upscaling, Random Walk Model

How to Cite:

Porta, G., Baioni, E., (2025) “Upscaling Transport and Sorption Processes via Spatial Markov Model in a Three-Dimensional Porous Domain”, ARC Geophysical Research (1), 12. doi: https://doi.org/10.5149/ARC-GR.1654