Flow morphology and patterns in porous media convection: A persistent homology analysis

- 1 Banner appropriate to article type will appear here in typeset article Flow morphology and patterns in porous media convection: A persistent homology analysis Marco De Paoli1,2†, Sergio Pirozzoli3 and Lou Kondic4 1Institute of Fluid Mechanics and Heat Transfer, TU Wien, 1060 Vienna, Austria 2Physics of Fluids Group and Max Planck Center for Complex Fluid Dynamics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217 7500AE Enschede, The Netherlands 3Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universit`a di Roma, Rome, Italy 4Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA (Received xx; revised xx; accepted xx) Convective mixing in porous media is crucial in both geophysical and industrial fields, spanning applications ranging from carbon dioxide sequestration to contaminant transport in groundwater. Key processes are affected by convective heat transport or diffusion of chemical species in porous formations. Intense convection flow and mixing create complex, dynamic patterns that are difficult to predict and measure. The present work focuses on the use of topological data analysis, in particular, the measures emerging from the growing field of persistent homology (PH), to quantify these patterns. These measures are objective and quantify structures across all temperature or concentration values simultaneously. These techniques, when applied to classical porous media setups, such as one-sided and Rayleigh- B´enard flow configurations, provide new insights into the system’s structure, flow patterns, and macroscopic mixing properties. Using large datasets we make publicly available, comprising original simulations as well as those presented in previous works, we correlate the behaviour of the heat transport rate (quantified by the Nusselt number) with the evolution of the flow structures (quantified by the PH measures). Finally, we provide a detailed analysis of the flow evolution over a wide range of governing parameters, namely the Rayleigh-Darcy number and the domain size. Key words: porous media, convection, topological data analysis, persistent homology 1. Introduction Transport of heat and chemical species in porous media is relevant to natural and industrial flows: from latent heat thermal energy storage systems (Trelles & Dufly 2003; Xu et al. 2017) to the formation of sea ice (Feltham et al. 2006; Wells et al. 2019), several key processes are controlled by the redistribution of heat and solutes in confined domains. When the motion is driven by density gradients within the fluid layer, and the density field depends † Email address for correspondence: marco.de.paoli@tuwien.ac.at arXiv:2512.21958v1 [physics.flu-dyn] 26 Dec 2025 2 De Paoli M., Pirozzoli S. & Kondic L. on the local distribution of the scalar (e.g., temperature or solute concentration), the flow is controlled by natural convection. Local density differences are contrasted by the dissipative mechanisms of friction (due to narrow pore spaces) and diffusion (which reduce the gradients of the scalar field), which, in turn, affect the flow field. The relative importance of driving (convection) and dissipative (diffusion, friction) mechanisms is quantified by the Rayleigh- Darcy number, Ra (hereinafter defined as Rayleigh number). A similar dynamics occurs in the presence of key geophysical systems, e.g., geothermal flows in underground sites (Hu et al. 2023), thawing of permafrost (Wang et al. 2025), dispersion of contaminants in groundwater flows (Simmons et al. 2001; De Paoli et al. 2025b), and storage of carbon dioxide (CO2) in saline aquifers. The latter, in particular, has been extensively studied in recent decades, due to its enormous relevance in mitigating the effects of climate change (Metz et al. 2005). Geological sequestration of carbon dioxide involves injecting large amounts of CO2 into underground geological formations for permanent storage. These formations can be idealized as porous, rocky matrices naturally filled with resident fluid (brine) and confined at the top and bottom by two impermeable layers. After injection, due to the density difference between carbon dioxide (≈500 kg/m3) and brine (≈1000 kg/m3), CO2 migrates to the top of the brine. Here, the impermeable rock layer prevents CO2 from rising further. This situation is potentially hazardous because, in the event of a fracture in this geological barrier, CO2 will eventually leak, reaching the upper layers and possibly returning to the atmosphere (Emami-Meybodi et al. 2015; Jin 2024). However, at the CO2- brine interface, mixing occurs, resulting in a denser fluid (CO2+brine) that eventually sinks, leading to additional carbon dioxide dissolution due to convection and permanently trapping CO2 (solubility trapping mechanism). A key question in assessing the suitability of potential sequestration sites is determining the CO2 mixing rate in brine. The archetypal system

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