Tag Archives: geophysical flows

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.

How to study the behaviour of microplastics?

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Microplastics are plastic fragments smaller than 5 mm originated from human activities, and have been found everywhere, also in the remotest places of the Earth. Measuring their position and velocity in turbulent flows, such as ocean, rivers and lakes, is crucial to better understand their behaviour and make physical models that describe their paths. To this aim, we designed a new facility, the TU Wien turbulent Water Channel, which we recently presented in paper published on Review in Scientific Instrument. This project is funded by FWF (Austrian Science Fund).

The TU Wien Turbulent Water Channel (main figure). Cameras may be arranged in different configurations to investigate the behaviour of microplastics (bottom right figure).

The TU Wien Turbulent Water Channel is a 3000 litres volume and 10 meters long flow loop designed for 3D and time-resolved measurements of anisotropic particles dynamics. We developed a novel approach to track microplastics, since they are usually anisotropic and techniques developed for spherical particles are not suitable to track such objects. In addition, in this work, we provide guidelines to design turbulent water ducts, and we also compare against existing facilities.

The data and the paper (Open Access) are freely available for download.

Would you like to perform experiments in the TU Wien Turbulent Water Channel? Contact us!

This work has been selected for the Kudos Research Showcase.

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

Summer School on Porous Media

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Udine, JULY 11, 2022 to JULY 15, 2022

26TH CISM-IUTAM INTERNATIONAL SUMMER SCHOOL ON “CONVECTION AND DEFORMATION IN POROUS MEDIA: GEOPHYSICAL AND BIOLOGICAL FLOWS”

This course is organised at CISM (Udine, Italy) and coordinated by Prof. Chris. MacMinn (University of Oxford) and me. All the details about the course are available here. You can download the flyer here.

Flow and transport in porous media are relevant for many geophysical, industrial, and biological applications, including carbon sequestration, glacial drainage, papermaking, transport across vascular walls, and bacteria motility. Predicting the evolution of these systems is difficult because of the interplay between different physical features, such as complex flow patterns, convection and reaction, and transformation of the porous matrix through deformation and phase change. In addition, flow and transport in porous media are governed by physical processes that span a wide range of length and time scales. Rapidly increasing computational power has recently enabled threedimensional, high-resolution and time-dependent simulations of these flows at both the pore-scale and the Darcy-scale, producing an entire branch of flourishing research into multiphase flow in porous media. Experimental progress has also been substantial, thanks to improved measurement techniques inboth 2D and 3D. Therefore, it is now useful to review the many studies on the subject to provide an overview of the current state of the art, and to put future research paths in perspective.
This course will provide an overview of the most up-to-date modelling approaches, numerical simulations, and experimental methods used to study the dynamics and properties of porous media flows characterized by convection and deformation.

Schematic representation of CO2 dissolution in saline aquifers

Fundamentals of transport in porous media will be presented, including upscaling techniques, thermodynamics of two-phase mixtures, Lagrangian interpretations, fractional diffusion, non-locality and memory.

Time-dependent evolution of convection-driven flows in different configurations will be analyzed, with reference to geophysical and industrial applications and with particular attention to the dynamics and structures of convection, effect of porous media properties on convection and transition from 2D to 3D convection. An overview of experimental and numerical techniques for convective flows in porous media will be presented and reviewed.

Principles of the coupling between flow, transport, and deformation in porous media will be presented. The small-deformation limit and classical linear poroelasticity will be discussed in the context of subsurface flows. Large-deformation poromechanics will be discussed in the context of polymeric hydrogels (including swelling and drying phenomena), paper-pulp suspensions (including viscoelasticity and plasticity), and granular media (including friction and rearrangement).
The implications of deformation for the dispersion and mixing of solutes will be considered. Two-phase flows will be considered, including capillary and wettability effects. Phase-field approaches will be introduced in the context of multiphase solidification problems (including ice, methane clathrates, and lava) and applied to the growth and migration of gas bubbles in soft porous media.

The course is addressed to graduate students and researchers in applied mathematics, physics and chemical/mechanical engineering.
The advanced topics and the presentation of current progress in this very active field will also be of considerable interest to senior researchers and industrial practitioners having a strong interest in understanding the multiscale complex behavior of such multiphase flows.

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