Tag Archives: convection

Convective mixing of carbon dioxide : 3D vs. 2D

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To mitigate the catastrophic effects of global warming, we will have to capture from the atmosphere billions of tons of carbon dioxide (CO2), and permanently store it underground. And there is no doubt about that. But what will it happen to carbon dioxide hundreds or thousands of meters underground? How long will it take for CO2 to mix with the resident fluid?

In our new paper, published on Geophysical Research Letters, we answer this question in the context of homogenous and isotropic rock formations. We used massively parallelized numerical simulations to systematically investigate the flow dynamics in 3D systems and provide a robust quantification of the differences occurring with respect to ideal 2D systems.

With this dataset, which we make freely available, we derive a simple, reliable and accurate physical model to describe the post‐injection dynamics of carbon dioxide. This model can be used to identify suitable sequestration sites or to design carbon dioxide injection strategies.

This project has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Sklodowska‐Curie grant agreement MEDIA No. 101062123. We acknowledge the EuroHPC Joint Undertaking (EuroHPC JU) for awarding the project GEOCOSE number EHPC‐REG‐ 2022R03‐207 and for granting access to the EuroHPC supercomputer LUMI‐C, hosted by the LUMI supercomputer consortium (Finland).

The 📕 paper and the 💻 data are freely available for download. Enjoy the convective cells in the movie below!

All the details are available here https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2025GL114804

Evolution of the near-wall flow structures for Rayleigh-Darcy number 10,000. The concentration distribution over a horizontal slice taken near the upper interface.  The convective time, 0 ≤ t ≤ 85, indicated in the top left corner, spans over all the regimes. Fingers appear at t ≈ 1. They subsequently merge into larger and statistically-steady cells (4 ≤ t ≤ 14). Finally, the driving reduces as a result of the domain saturation, and the near-wall cells dynamics slows progressively down.

Pore-scale analysis of convective mixing in porous media

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Mixing in porous media is a non-linear process. The flow is coupled to the porous matrix, but the flow structures may be much larger than the characteristic pore size. These finger-like structures form, grow and merge, and control the mixing process. In this multiphase and multiscale system, making accurate predictions is a challenging task. Mixing is controlled by the combined action of convection, diffusion and viscous dissipation. With the aid of experiments and simulations, we studied this complex system and provide simple physical models describing the flow evolution in all the stages of the mixing process.

Experiments consists of bead packs and two miscible fluids of different color. In the simulations, we combined multiple grid resolutions and immersed boundaries method to resolve high-Schmidt number flows in the pore-space. Finally, we use these results to gain a quantitative understanding of the flow evolution, and in particular of the mixing.

The paper and the data are freely accessible.

What does the image above represent? It is obtained from experimental measurements of the interface. The evolving interface between the fluids is tracked. The color changes with time, and as a results this figure contains information about the entire flow evolution. The movie below shows how the interface is tracked. Do you want to know more? Contact me!

This work was funded by the European Union’s Horizon Europe research and innovation programme under the Marie Sklodowska-Curie grant agreement MEDIA no. 101062123, the Max Planck Center for Complex Fluid Dynamics, PRACE (project 2021250115) and the Austrian Science Fund (FWF) (J-4612).

Review paper published in The European Physical Journal E

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Can we predict the formation of sea ice? And the dissolution of CO2 in geological reservoirs? These phenomena are controlled by convective motions in a porous medium. In this review article fresh off the presses, published in The European Physical Journal E, I present recent advances on convection in porous media, a paramount topic for climate change and energy transition. The paper (Open Access) is freely available for download at here.

When a porous medium is filled with two fluid layers of different density, with the heavier fluid sitting on top of the lighter one, the system may become unstable. Due to the vertical density contrast, convective finger-like structures can form and accelerate fluid mixing. This configuration is representative of a variety of systems of practical interest, particularly in geophysical processes.

The regular polygonally patterned ridges observed in dry salty lakes are the surface signature of the convective transport of salt in the subsurface porous soil, a fundamental process in arid regions. Formation of sea ice or solidification of multicomponent alloys may originate mushy layers, which consist of porous media filled by a multicomponent fluid subject to density gradients. It follows that the consequent convective motions control the solidification dynamics. The long-term storage of carbon dioxide in underground geological formations is also driven by convection. These examples are representative of why understanding convective mixing in porous media is crucial, for instance, to tackle grand societal challenges like energy transition, or to predict how environmental systems respond to climate change.

The fluid mechanics underlying porous media convection is made complex by the multiscale and multiphase character of the flow. As a result, a combination of different complementary approaches has been deployed to elucidate the intricate physics of convection in porous media. This work reviews recent numerical, experimental, and theoretical findings, discusses their limits of applicability, and highlights possible future research directions.

Experiments on convection in porous media

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Solute transport and dispersion in underground geological formations play a key role in hydrology and geophysics, from carbon sequestration to water contamination. Understanding the underlying fluid dynamics is crucial to make reliable long-term predictions of the evolution of these systems. In this work, published on Physical Review Fluids and partially funded by the Austrian Science Fund (FWF), we investigate experimentally the role of convection on solute transport in confined porous media.

We assess experimentally the existence of a superlinear scaling for the growth of the mixing region in a confined porous medium. We employ an optical method to obtain high-resolution measurements of the density fields in Hele-Shaw flows, and we perform experiments for large values of the Rayleigh-Darcy number. We can confirm that the growth of the mixing length during the convection-dominated phase follows the scaling predicted by previous two-dimensional simulations. 

Thank you Diego Perissutti (visiting Master student at TU Wien at the time of the experiments, now PhD candidate at the University of Udine), Cristian Marchioli (University of Udine) and Alfredo Soldati (TU Wien and University of Udine) for the collaboration. This work has been partially performed at the University of Twente, Physics of Fluids Group.

In the movie, you can see the evolution of the finger number for one of the experiments considered.  Article, visualizations, and data about this work are available here:

[1] De Paoli et al., arXiv:2206.13363 (2022), https://arxiv.org/abs/2206.13363
[2] De Paoli et al., Phys. Rev. Fluids 7, 093503 (2022), https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.093503
[3] De Paoli et al., Data and figures in MatLab format, https://doi.org/10.6084/m9.figshare.19761766.v3
[4] Movie 1 https://youtu.be/njuebV7mLxw
[5] Movie 2 https://youtu.be/lC8Xbfal4J0

What is the flow topology of a convective porous media flow?

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What is the minimum domain size we need to simulate to capture the large-scale flow structures?

We have addressed these questions in our recent work published on Journal of Fluid Mechanics. With the aid of massively parallelized numerical simulations, we show that the near-wall, large-scale temperature patterns (supercells) represent the footprint of the flow structure in the core of the domain (megaplumes). We have also analyzed the effect of the domain size (aspect ratio, AR), on the resulting flow topology.