Ra incorporation into (Ba,Ra)SO4 solid solutions is a key control on Ra mobility in groundwater systems and typically occurs through coprecipitation and recrystallization. The effectiveness and persistence of these mechanisms under long-term reactive transport conditions remain poorly constrained, particularly in fractured crystalline rocks, where Ra migration is controlled by the coupled effects of heterogeneous flow, advective-diffusive transport, fracture-matrix mass exchange, reaction kinetics, and evolving hydrogeochemical conditions. Here, we employ 3D reactive transport modeling using PFLOTRAN to investigate Ra mobility under near-field conditions relevant to geological nuclear waste repositories. The models couple fluid flow, solute transport, and non-ideal solid solution-aqueous solution (SS-AS) interactions, incorporating a regular Guggenheim solid solution model and composition-dependent dissolution-precipitation kinetics for stoichiometric solid solutions. Simulations are conducted in a 10 m & times; 10 m & times; 10 m fracture-matrix domain upscaled from a discrete fracture network, with a constant-flux inflow boundary and fixed Ra concentration representing a sustained Ra source over 10,000 years. The results show that coprecipitation leads to strong but transient Ra immobilization, with substantial Ra uptake within the first similar to 200 years, followed by progressive Ra remobilization as sulfate is depleted and previously formed solid solutions dissolve. Consequently, Ra retention decreases markedly and becomes minimal after similar to 1000 years. In contrast, recrystallization supports persistent Ra immobilization throughout the entire 10,000-year simulation period, provided that sufficient barite remains available within fracture zones. This mechanism is sustained by kinetically controlled coupled dissolution-reprecipitation and produces a characteristic spatial zonation, with Ra-rich solid solutions near inflow regions and progressively Ba-rich compositions downstream. Sensitivity analyses further demonstrate that increasing Ba/Ra ratios in the inflowing fluid can reduce the long-term Ra retention under kinetically controlled reactive transport conditions, in contrast to predictions based solely on thermodynamic equilibrium. Fractures are identified as the dominant domains for long-term Ra immobilization, whereas the low-permeability matrix contributes only minimally due to limited diffusive accessibility. Once fractures lose their retention capacity, aqueous Ra is predominantly flushed from the system rather than retained within the matrix. Overall, these results suggest that equilibrium assumptions commonly adopted in radionuclide safety assessments are insufficient to predict Ra behavior in complex subsurface systems, and thus robust evaluation of long-term Ra mobility requires coupling reaction mechanisms and kinetics with flow and transport in evolving fracture-matrix systems. Although both coprecipitation and recrystallization form (Ba,Ra)SO4 solid solutions, their distinct microscopic mechanisms lead to contrasting long-term behaviors when upscaled to the field scale. These findings have important implications for nuclear waste disposal and managing Ra contamination in geothermal and mining environments.

Microfluidics experiments offer high-resolution insights into transport and chemical processes in porous media, yet direct measurement of evolving concentration profiles remains challenging. Numerical simulations can serve as virtual probes but are labor-intensive and computationally expensive. Here, we develop a physics-based machine learning toolbox that transforms such simulations into efficient and scalable virtual probes. Central to our toolbox is the non-intrusive reduced basis method, supported by the U-Net and the Convolutional Autoencoder, which learns mappings from experimental images and physical parameters to concentration profiles. By incorporating physics into its construction, the toolbox delivers accurate predictions with a limited number of training samples. Applied to two microfluidics experiments with different base patterns, the toolbox predicts spatio-temporal concentration profiles, effective diffusivities, and locations with a high probability of precipitation. This paves the way for digital twins that enable real-time analysis and tuning of experiments on the fly.

The transition to a sustainable, low-carbon energy future requires transformative advancements in energy and environmental technologies. Carbon capture and sequestration, underground hydrogen storage, and nuclear waste geological disposal will be central aspects of a sustainable energy future, both for mitigating CO2 emissions and providing green energy. A comprehensive understanding of multiphase flow through porous media, along with reactive transport and microbial activities, is essential for assessing the feasibility and managing the risks of these technologies. Microfluidic porous media platforms have emerged as powerful tools for the direct visualization of multiphase reactive flow in porous media and eventually optimizing these multiple physicochemical and biological processes. This review highlights critical scientific challenges associated with these sustainable energy solutions and summarizes the state-of-the-art microfluidic techniques for studying the interplay between multiphase flow, reactive transport, and biological effects in porous media. We provide a comprehensive overview of how these microfluidic approaches enhance the understanding of fundamental pore-scale dynamics and bridge the gap between pore-scale events and large-scale processes. This review is expected to promote both experimental and theoretical understanding of multiphase reactive flow in porous media, thereby informing material design, process optimization, and predictive modeling for scalable implementation. By fostering interdisciplinary collaboration across microfluidics, fluid mechanics, geophysics, materials science, and subsurface engineering, we hope to accelerate innovation and advance sustainable energy solutions.

This study investigates the interlayer diffusion dynamics in sodium montmorillonite (Na-MMT), a smectite clay with significant applications in environmental science, pharmaceuticals, and advanced materials. We present a multiscale computational framework that integrates atomistic simulations with mesoscale modelling to explore the influence of interlayer and free pores on water and ion diffusion under varying dry densities (0.8–1.3 g/cm^3). The model incorporates experimentally determined platelet size distributions and explicitly accounts for polydispersity and anisotropic transport. The study results reveal that interlayer pores contribute minimally to overall water diffusion at the studied dry densities. Water diffusion predominantly occurs through free pores, with diffusion scaling factors closely aligning with experimental tritium tracer measurements when interlayer throttling was considered. The study also highlights the anisotropic nature of diffusion in Na-MMT, with diffusion parallel-to-compaction being significantly slower than in the normal direction which is consistent with experiments. The computational model, validated against lattice Boltzmann simulations and experimental data, provides insights into the geometric tortuosity and pore size distribution of Na-MMT. Despite its limitations, such as the absence of three-water minima energy profiles and rigid platelet assumptions, the model offers a robust framework for understanding nanoconfined diffusion. Future work will focus on refining interlayer energy profiles and incorporating flexible platelet dynamics to enhance predictive accuracy with implications for optimizing materials in environmental, industrial, and biomedical applications.

Previous studies claimed that the non-monotonic effects of wettability came mainly from the heterogeneity of geometries or flow conditions on multiphase displacements in porous media. For macroscopic homogeneous porous media, without permeability contrast or obvious preferential flow pathways, most pore-scale evidence showed a monotonic trend of the wettability effect. However, this work reports transitions from monotonic to non-monotonic wettability effects when the dimension of the model system rises from two-dimensional (2-D) to three-dimensional (3-D), validated by both the network modelling and the microfluidic experiments. The mechanisms linking the pore-scale events to macroscopic displacement patterns have been analysed through direct simulations. For 2-D porous media, the monotonic effect of wettability comes from the consistent transition pattern for the full range of capillary numbers $Ca$ , where the capillary fingering mode transitions to the compact displacement mode as the contact angle $\theta$ decreases. Yet, it is indicated that the 3-D porous geometries, even though homogeneous without permeability contrast or obvious preferential flow pathways, introduce a different $Ca$ – $\theta$ phase diagram with new pore-scale events, such as the coupling of capillary fingering with snap-off during strong drainage, and frequent snap-off events during strong imbibition. These events depend strongly on geometric confinements and capillary numbers, leading to the non-monotonicity of wettability effects. Our findings provide new insights into the multiphase displacement dependent on wettability in various natural porous media and offer design principles for engineering artificial porous media to achieve desired immiscible displacement behaviours.

The safety assessment of deep geological disposal of nuclear waste requires a sound understanding of radionuclide retention in the repository host rocks. Here, we investigate the retention behaviour of the safety relevant radionuclide 226Ra in the heterogeneous sandy facies of the Opalinus Clay (OPA-SF) at the Mont Terri underground rock laboratory. Various rock samples were selected from a drill core (BAD-1) located in the lower sandy facies, which were representative for its textural and mineralogical heterogeneity. The samples were carefully characterized with respect to mineralogy and chemistry using X-Ray diffraction and electron microscopy. The amounts of quartz, carbonates and clay minerals in the samples ranged between 58 wt.% – 65 wt.%, 13 wt.% – 35 wt.% and 5 wt.% – 25 wt.%, respectively, underpinning the mineralogical heterogeneity. Rare (Ba,Sr)-sulphate precipitates were identified in the clay matrix by electron microscopy. The uptake behaviour of Ra was evaluated using batch sorption experiments. Corresponding to the mineralogical variability of the rock samples, the measured distribution ratios Rd for the 226Ra retention varied between 20 L·kg-1 and 260 L·kg-1 after 120 days. The experimental results and thermodynamic modelling approaches suggest that various processes contribute to the uptake of 226Ra on different time scales: fast cation exchange and surface complexation reactions by clay minerals and the (slower) formation of solid solutions during recrystallization of (Ba,Sr)-sulphates as well as retention by carbonate minerals; the latter mechanism still requiring further investigation.

Abstract Solute diffusion in partially saturated porous media is an important fundamental process in many natural and environmental systems. At low water saturation, the solute transport is governed by the diffusion in thin water films on the surfaces of solids. In this study, we established an improved pore‐scale simulation framework successfully describing the solute diffusion in variably saturated porous media (e.g., soils), which considers the contribution of the diffusion within the thin water film on the surface of the solid matrix. The model takes into account the liquid–gas distribution in the underlying porous media by the Shan‐Chen lattice Boltzmann Method (LBM) and simulates the solute diffusion in the bulk liquid phase and the water film. Based on the numerical results, an easy‐to‐use theoretical formula was also developed to predict the effective diffusivity in microporous materials at low saturation levels. The average relative error of its prediction with respect to the experimental data from the literature is about 30%, while that of the classical power law exceeds 70%. A simple phase diagram was defined, which allows us to identify the situations under which it is necessary to take the influence of surface water films on the effective diffusivity in unsaturated microporous media into account. The present study improves the pore‐scale model to address solute diffusion in the water films at low water saturation and elucidates the contribution of thin water films on solute transport.

An accurate mechanistic understanding of solute diffusion in partially saturated clays is critical for assessing the safety of deep geological repositories for radioactive waste. In this study, a pore-scale numerical framework is developed to simulate water and ion diffusion in partially saturated clays. First, the two-phase Shan-Chen Lattice Boltzmann method is employed to establish the liquid-gas distribution in a reconstructed three-dimensional pore geometry of a clay. An equivalent solute method is also developed and validated to improve the numerical stability of the solution at the liquid/gas interface corresponding to steep variations of the concentration and diffusion coefficient of the water tracer. By using a mobility-distance relationship from molecular simulations, Fick's law is numerically solved to simulate water diffusion in nanopores, while the coupled Poisson-Boltzmann-Nernst-Planck equations are solved to simulate ion diffusion under the influence of the electrical double layer (EDL). Our model reveals that the decrease of relative effective diffusion coefficients during the desaturation is more pronounced for ions than for water, due to the additional transport pathway of water tracers in the gas phase. The obtained effective diffusion coefficients of tritiated water and ions agree well with reported data from compacted sedimentary rocks. By comparing the local electric potential and the distribution of ion concentrations in single pores, the simulation results suggest that the EDL in unsaturated clays has a more complex influence on ion distribution than under fully water-saturated conditions. This study provides critical insights into the coupled transport processes of solutes in partially saturated clays. Development of a pore-scale numerical framework to simulate water and ion diffusion in partially saturated claysDerivation of an equivalent solute method to improve the numerical stability caused by the discontinuities at the water/vapor interfaceThe electrical double layer has a stronger effect on ion transport under unsaturated conditions than under water saturated conditions

Potential evaporation (PE) is a significant input in many hydrological models for the estimation of actual evaporation. Evaporation from water (PEw) is generally considered equivalent to evaporation from saturated bare soils (PEs). The influences of the underlying surface on PE as well as the energy and vapour transfer in potential evaporation processes over different surfaces are rarely discussed. In this research, lysimeter experiments were set up to measure the diurnal cycles of evaporation from two saturated sandy soils and water at a high temporal resolution in the Guanzhong Basin, China. Evaporation from Class A Pan, meteorological variables and temperatures were also measured during the experiment. Observation results show that PEs is similar to 12% higher than PEw on a yearly scale. There were also some clear differences in diurnal and seasonal PE dynamics between saturated bare soils and water. In summer, PEs is higher than PEw at day but smaller at night, with the peak value of PEw lagging similar to 4 h behind PEs. These observed PE dynamics and energy transfer processes can be quantitative explained on the basis of a full analysis of the energy balance equation. A comprehensive description of the flux transfer processes showed that these differences in PE are governed by differences in available energy (including albedo and thermal properties) between soils and water. Moreover, the observed differences in PE and vapour transfer processes were reproduced and described by improving the vapour diffusion equation, with considering the influence of different surfaces and boundary layer thicknesses. It is found that dynamics in PE were mainly characterised by surface temperature, which further determined the vapour gradients between the evaporation surface and air flow. The results suggested that differences between PEs and PEw cannot be neglected in hydrological applications. This study can act as both an experimental and theoretical reference for estimating potential evaporation rates.

Abstract. Deep geological repositories with a multi-barrier concept are foreseen by various countries for the disposal of high-level radioactive waste. Simulation tools for a close-to-reality description of repository evolution scenarios are required, especially to resolve the challenging task of comparing and assessing the long-term safety of different repository concepts in different host rocks within the German site-selection process. Chemical, thermal, and pressure gradients at the interfaces of the different barriers in a repository can lead to mineral dissolution and precipitation, generating non-linear responses in transport and mechanical properties of barrier materials and host rocks. Reactive transport modeling (RTM) can be applied to investigate these perturbations and processes across temporal and spatial scales to assess subsurface evolution. Nevertheless, implementing RTM at the continuum scale while accounting for pore-scale heterogeneities and geometry evolution remains a challenge. Pore-scale simulations offer the potential to capture the complex evolution of porous media over a broad range of Peclet and Damköhler numbers, and they can be utilized to improve the RTM by using upscaling methods (Prasianakis et al., 2020). In this context, we developed “lab-on-a-chip” experiments, combining time-lapse high-resolution optical microscopy and confocal Raman spectroscopy to test extended constitutive equations to classically employed Archie's law to improve the description of changes in transport properties (e.g., diffusivity) in evolving porous media in RTM. The 3D Raman tomography of the porous media combined with pore-scale modeling enabled the derivation of upscaled transport parameters. Our results highlight the importance of calibrating pore-scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers, whose results can be further used for the derivation of upscaled modeling parameters. The derived and parameterized constitutive equations based on simple systems have been tested in reactive transport models as a sensitivity case study to evaluate uncertainties in the predictions of the evolution of real subsurface systems such as clay–cement interfaces in deep geological repositories.

Understanding mineral precipitation induced porosity clogging and being able to quantify its non‐linear feedback on transport properties is fundamental for predicting the long‐term evolution of energy‐related subsurface systems. Commonly applied porosity‐diffusivity relations used in numerical simulations on the continuum‐scale predict the case of clogging as a final state. However, recent experiments and pore‐scale modeling investigations suggest dissolution‐recrystallization processes causing a non‐negligible inherent diffusivity of newly formed precipitates. To verify these processes, we present a novel microfluidic reactor design that combines time‐lapse optical microscopy and confocal Raman spectroscopy, providing real‐time insights of mineral precipitation induced porosity clogging under purely diffusive transport conditions. Based on 2D optical images, the effective diffusivity was determined as a function of the evolving porous media, using pore‐scale modeling. At the clogged state, Raman isotopic tracer experiments were conducted to visualize the transport of deuterium through the evolving microporosity of the precipitates, demonstrating the non‐final state of clogging. The evolution of the porosity‐diffusivity relationship in response to precipitation reactions shows a behavior deviating from Archie's law. The application of an extended power law improved the description of the evolving porosity‐diffusivity, but still neglected post‐clogging features. Our innovative combination of microfluidic experiments and pore‐scale modeling opens new possibilities to validate and identify relevant pore‐scale processes, providing data for upscaling approaches to derive key relationships for continuum‐scale reactive transport simulations.

Accurate modeling and simulation of radionuclide migration in clay rocks such as the Opalinus Clay (OPA) play a key role in the safety assessment of deep geological repositories for nuclear wastes. At the continuum scale, the representative elementary volume (REV) is a fundamental constraint to quantify the effective diffusivity, which is a key parameter in reactive transport (RT) models. Therefore, an accurate estimation of the REV is essential for a meaningful continuum‐scale RT simulation in heterogeneous clay rocks. This study presents a comprehensive analysis of the heterogeneities of porosity and effective diffusivity in clay rocks by using the classical sampling theory and pore‐scale simulations. First, in this study, the two‐dimensional representative elementary area is correlated with the REV for porosity via a characteristic length. Next, it is shown that the REV for diffusivity is larger than the REV for porosity. Moreover, these two REVs can be correlated using Archie's law. In such a way, the REV for diffusivity can be determined by the developed correlations through analyzing two‐dimensional microstructures, thus significantly reducing the computational cost. Finally, the applicability of our approach for clay rocks is validated by experimental data on the diffusion of tritiated water in the heterogeneous sandy facies of OPA. From both the experimental data and the modeling prediction, the REV for diffusivity in the sandy facies of OPA is in the order of cubic centimeters. This study provides critical insights into the diffusion in heterogeneous clay rocks toward an enhanced predictability of radionuclide migration.

Geological repositories for nuclear waste are based on multi-barrier concepts, combining engineered materials with a suitable host rock. Chemical and thermal gradients at barrier interfaces can lead to mineral precipitation, resulting in a reduction of porosity and potentially leading clogging, which significantly affects the diffusivity of the porous media [1]. A process understanding of porosity clogging and its effect on macroscopic transport properties is thus essential for a reliable assessment of the evolution of the repository. Although in the context of nuclear waste disposal, a porosity reduction appears desirable to inhibit radionuclide migration, it can be detrimental, particularly in the case of corrosion-induced gas generation [2]. So far, mechanisms and kinetics of clogging are poorly understood, challenging the predictive capabilities of reactive transport models. Recent experiments conducted to benchmark continuum-scale models revealed the inadequacy of conventional porosity-diffusivity relationships (Archie's law) to account for changes in effective diffusivity of evolving porous media [1]. Further pore-scale modelling investigations suggested an inherent diffusivity of newly formed precipitates [3]. To verify this hypothesis, we developed a “lab-on-a-chip” approach [4] to decipher clogging phenomena, combining time-lapse optical microscopy and confocal Raman spectroscopy. The microfluidic device consisted of a 2D pore network linked to two supply channels which enabled the diffusive mixing of Sr 2+ aq and SO 4 2- aq ions, triggering the precipitation of celestine. As the pore network became clogged, the

Understanding of thermal effects on ion transport in porous media is very important for environmental applications. The movement of ions along a temperature gradient is named thermophoresis or thermodiffusion. In nanoporous media, where the interaction of ions with solid-liquid interfaces has a significant influence on their migration, the theoretical understanding of thermodiffusion is still incomplete. Herein, we present experimental results for the thermodiffusion of cations in saturated nanoporous silica by the through-diffusion method. Both the experimental data and theoretical analysis indicate that the temperature-induced polarization of surface charges strongly influences ionic transport. Stated simply, the electric field in a liquid electrolyte confined in nanopores changes when the applied temperature gradients are altered, thereby affecting the motion of the nanoconfined ionic species. By applying an external temperature field, the gradient of the surface charge density leads to the charged aqueous species exhibiting strong temperature gradient-dependent electrophoretic mobility. When the thickness of the electrical double layer is comparable to the size of the nanopores, the theory used herein indicates that this kind of nonisothermal ionic mobility is up to one order of magnitude larger than classical thermophoretic mobility. This study improves the understanding of the underlying mechanisms that govern the transport of ions in nanoporous media, which could set the stage for diffusional metamaterials induced by specific thermal fields.

Reactive transport modelling is a powerful tool to assess subsurface evolution in various energy-related applications. Upscaling, i.e., accounting for pore scale heterogeneities into larger scale analyses, remains one of the biggest challenges of reactive transport modelling. Pore scale simulations capturing the evolutions of the porous media over a wide range of Peclet and Damköhler number in combination with machine learning are foreseen as an efficient methodology for upscaling. However, the accuracy of these pore scale models needs to be tested against experiments. In this work, we developed a lab on a chip experiment with a novel micromodel design combined with operando confocal Raman spectroscopy, to monitor the evolution of porous media undergoing coupled mineral dissolution and precipitation processes due to diffusive reactive fluxes. The 3D-imaging of the porous media combined with pore scale modelling enabled the derivation of upscaled transport parameters. The chemical reaction tested involved the replacement of celestine by strontianite, whereby a net porosity increase is expected because of the smaller molar volume of strontianite. However, under our experimental conditions, the accessible porosity and consequently diffusivity decreased. We propose a transferability of the concepts behind the Verma and Pruess relationship to be applied to also describe changes of diffusivity for evolving porous media. Our results highlight the importance of calibrating pore scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers of which results can be further used for the derivation of upscaled parameters.

Abstract. Deep geological repositories with a multi-barrier concept are foreseen byvarious countries for the disposal of high-level radioactive waste. A reliableand consistent assessment of the safety of these repositories over time scalesof some hundred thousand years requires an advancement of processunderstanding. Simulation tools need to be developed for a close-to-realitydescription of repository evolution scenarios. This is especially required toresolve the challenging task of comparing and assessing the safety ofdifferent repository concepts in different host rocks within the Germansite-selection process. The construction of underground galleries andgeotechnical barriers in the host rock formation and the emplacement ofnuclear waste packages will create perturbations induced by chemical, thermaland pressure gradients at the interfaces of the different barriers, leading tomineral dissolution and precipitation to achieve re-equilibration. Suchcoupled hydrogeochemical processes generate non-linear responses in transportand mechanical properties of barrier materials and host rocks, which have tobe taken into account for a more rigorous assessment of repository systemevolution. Reactive transport modeling (RTM) can be applied to investigate theseperturbations and processes across temporal and spatial scales, from themicro-scale at interfaces via the repository near field to the entirerepository system – information not accessible through experimentsalone. Although RTM is capable of addressing highly complex hydrogeochemicalphenomena, the application of RTM codes to real systems is impeded by theoften simplified description of coupled processes. To enhance the predictivecapabilities of reactive transport models and to gain fundamental insightsinto the coupling between solute and radionuclide transport properties (e.g.,permeability and diffusivity) of porous media and dissolution/precipitationprocesses, we conducted experiments on “simplified” chemical systemscombined with pore-scale and continuum-scale reactive transport modelling tostudy processes in isolation, with the final aim of improving conceptualapproaches for process couplings implemented in reactive transport codes. In this context, we investigated the effects of coupled mineral dissolutionand precipitation in porous media on changes in permeability usingflow-through experiments conducted in a magnetic resonance imaging scanner,which enabled the in situ investigation of porosity evolution in combinationwith monitoring changes in permeability and mineralogy. Our observationsshowed that classical implementations in reactive transport codes such as theKozeny–Carman equation (Carman, 1937) failed to reproduce the changes inpermeability and that more sophisticated approaches are required (Poonoosamyet al., 2020a, b). Moreover, we developed a novel “lab-on-a-chip” setup,i.e., micronized counter diffusion reactors with in operando 3D Ramantomography (Poonoosamy et al., 2019, 2020c), which enables evaluation of thealteration in pore architecture and study of the effect of coupled mineraldissolution and precipitation on the diffusive transport of solutes andradionuclides in porous media. Our approach enables the development ofprocess-based theoretical models which allow for improvements in RTM codes andfor predicting the evolution of perturbed interfaces in waste repositories,thus building confidence in the predictive capabilities of reactive transportmodels and reducing uncertainties with respect to future repository evolution.