arXiv subjects

Marco De Paoli

Publications and source records attributed to Marco De Paoli.

10 recordsLinked to original sources

arXiv2026

How modeling assumptions shape predictions of convective mixing of carbon dioxide

We investigate how models of fluid properties and boundary conditions influence predictions of convective mixing in confined porous media, with relevance to subsurface carbon dioxide storage. Using high-resolution simulations at high Rayleigh-Darcy numbers (O($10^4$)), we analyze miscible fluids with linear, nonlinear, and non-monotonic density-concentration relationships under fixed- and free-interface in 2D and 3D. We show that, across all cases, mixing is quantified by the mean scalar dissipation, providing a unifying framework for convective-diffusive interactions. The density-concentration relationship affects mixing via the effective density contrast driving convection and the position of the maximum density. Free interfaces enhance early-time mixing through deformation, while long-term behavior depends on fluid properties and dimensionality. We demonstrate that simplified modeling assumptions (e.g., monotonic density laws or 2D flow) can lead to deviations in predicted mixing rates of up to O(10-100)%. These results offer guidance for model selection and improving predictions of convective mixing in geophysical systems.

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arXiv2026

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

Convective mixing in porous media is crucial in both geophysical and industrial fields, spanning applications ranging from carbon dioxide sequestration to geothermal energy extraction. 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-Bénard 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.

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arXiv2026

Universal transport laws in buoyancy-driven porous mixing

Buoyancy-driven convection in porous media governs heat and mass transport in a wide range of natural and engineered systems, from groundwater aquifers and geothermal reservoirs to carbon storage in geological formations and flows through planetary interiors. Yet the transient regime, in which fingering flows emerge and transport is strongly enhanced, is still described largely through empirical scaling laws, limiting predictive capability across conditions. Here we show that transient porous buoyancy-driven mixing obeys exact time-dependent balances that couple transport, flow intensity, and scalar dissipation. These balances remain accurate when restricted to the actively mixing layer, revealing that the essential dynamics are localized within a finite region. Leveraging these results, we derive a minimal one-parameter closure for the mean scalar field. The theory we propose predicts self-similar mean profiles, universal second-order statistics, and a linear transport law without case-by-case tuning. Direct numerical simulations up to spatial resolution of $2048\times2048\times16384$ points validate these predictions. Our results place transient porous mixing on a predictive footing, showing how macroscopic transport laws emerge from exact balances and self-similar dynamics, and provide a general framework for buoyancy-driven transport in porous media.

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arXiv2025

Solute mixing in porous media with dispersion and buoyancy

We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh-Taylor instability in which the presence of a solute produces density differences driving the flow. The effect of dispersion is modelled using an anisotropic Fickian dispersion tensor (Bear, J. Geophys. Res. 1961). In addition to molecular diffusion ($D_m^*$), the solute is redistributed by an additional spreading, in longitudinal and transverse flow directions, which is quantified by the coefficients $D_l^*$ and $D_t^*$, respectively, and it is produced by the presence of the pores. The flow is controlled by three dimensionless parameters: the Rayleigh-Darcy number $Ra$, defining the relative strength of convection and diffusion, and the dispersion parameters $r=D_l^*/D_t^*$ and $Δ=D_m^*/D_t^*$. With the aid of numerical Darcy simulations, we investigate the mixing dynamics without and with dispersion. We find that in absence of dispersion ($Δ\to\infty$) the dynamics is self-similar and independent of $Ra$, and the flow evolves following several regimes, which we analyse. Then we analyse the effect of dispersion on the flow evolution for a fixed value of the Rayleigh-Darcy number ($Ra=10^4$). A detailed analysis of the molecular and dispersive components of the mean scalar dissipation reveals a complex interplay between flow structures and solute mixing. The proposed theoretical framework, in combination with pore-scale simulations and bead packs experiments, can be used to validate and improve current dispersion models to obtain more reliable estimates of solute transport and spreading in buoyancy-driven subsurface flows.

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arXiv2025

Simulation and modelling of convective mixing of carbon dioxide in geological formations

We perform large-scale numerical simulations of convection in 3D porous media at Rayleigh-Darcy numbers up to $Ra=8\times10^4$. To investigate the convective mixing of carbon dioxide (CO$_2$) in geological formations, we consider a semi-infinite domain, where the CO$_2$ concentration is constant at the top and no flux is prescribed at bottom. Convection begins with a diffusion-dominated phase, transitions to convection-driven solute finger growth, and ends with a shutdown stage as fingers reach the bottom boundary and the concentration in the system increases. For $Ra \ge 5\times10^3$, we observe a constant-flux regime with dissolution flux stabilizing at 0.019, approximately 13\% higher than in 2D estimates. Finally, we provide a simple and yet accurate physical model describing the mass of solute entering the system throughout the whole mixing process. These findings extend solutal convection insights to 3D and high-$Ra$, improving the reliability of tools predicting the long-term CO$_2$ dynamics in the subsurface.

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arXiv2024

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh-Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, 2D DNS and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers, and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centre-line mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed: (i) The evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface; (ii) when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase; (iii) when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely length scale of diffusion, pore size, and domain height.

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arXiv2024

Full rotational dynamics of plastic microfibers in turbulence

The motion, settling, and dispersion of microplastics in the ocean are determined by their rotational dynamics. We present experiments on elongated, large aspect ratio, and mildly curved plastic fibers slightly longer than the Kolmogorov length scale. Exploiting their uniquely identifiable three dimensional orientation, we perform original optical Lagrangian investigations and provide a set of homogeneous data on their rotation rates around their longitudinal axis -- spinning rate -- and transversal axes -- tumbling rates -- which we explain in the context of the general features of turbulence.

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arXiv2024

Transport scaling in porous media convection

We present a theory to describe the Nusselt number ($Nu$), corresponding to the heat or mass flux, as a function of the Rayleigh--Darcy number ($Ra$), the ratio of buoyant driving force over diffusive dissipation, in convective porous media flows. First, we derive exact relationships within the system for the kinetic energy and the thermal dissipation rate. Second, by segregating the thermal dissipation rate into contributions from the boundary layer and the bulk, which is inspired by the ideas of the Grossmann and Lohse theory (J. Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001), we derive the scaling relation for $Nu$ as a function of $Ra$ and provide a robust theoretical explanation to the empirical relations proposed in previous studies. Specifically, by incorporating the length scale of the flow structure into the theory, we demonstrate why heat or mass transport differs between two-dimensional and three-dimensional porous media convection. Our model is in excellent agreement with the data obtained from numerical simulations, affirming its validity and predictive capabilities.

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arXiv2023

Convective mixing in porous media: A review of Darcy, pore-scale and Hele-Shaw studies

Convection-driven porous media flows are common in industrial processes and in nature. The multiscale and multiphase character of these systems and the inherent non-linear flow dynamics make convection in porous media a complex phenomenon. As a result, a combination of different complementary approaches, namely theory, simulations and experiments, have been deployed to elucidate the intricate physics of convection in porous media. In this work, we review recent findings on mixing in fluid-saturated porous media convection. We focus on the dissolution of a heavy fluid layer into a lighter one, and we consider different flow configurations. We present Darcy, pore-scale and Hele-Shaw investigations inspired by geophysical processes. While the results obtained for Darcy flows match the dissolution behaviour predicted theoretically, Hele-Shaw and pore-scale investigations reveal a different and tangled scenario in which finite-size effects play a key role. Finally, we present recent numerical and experimental developments and we highlight possible future research directions. The findings reviewed in this work will be crucial to make reliable predictions about the long-term behaviour of dissolution and mixing in engineering and natural processes, which are required to tackle societal challenges such as climate change mitigation and energy transition.

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arXiv2022

Experimental assessment of mixing layer scaling laws in Rayleigh-Taylor instability

We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling for the growth of the mixing region, which was observed in recent two-dimensional simulations. To this purpose, we use a Hele-Shaw cell. The flow configuration consists of a heavy fluid layer overlying a lighter fluid layer, initially separated by a horizontal, flat interface. When small perturbations of concentration and velocity fields occur at the interface, convective mixing is eventually produced: Perturbations grow and evolve into large finger-like convective structures that control the transition from the initial diffusion-dominated phase of the flow to the subsequent convection-dominated phase. As the flow evolves, diffusion acts to reduce local concentration gradients across the interface of the fingers. When the gradients become sufficiently small, the system attains a stably-stratified state and diffusion is again the dominant mixing mechanisms. We employ an optical method to obtain high-resolution measurements of the density fields and we perform experiments for values of the Rayleigh-Darcy number (i.e., the ratio between convection and diffusion) sufficiently large to exhibit all the flow phases just described, which we characterize via the mixing length, a measure of the extension of the mixing region. We are able to confirm that the growth of the mixing length during the convection-dominated phase follows the superlinear scaling predicted by previous simulations.

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