When confining granular materials, vertical stresses are redirected toward the sidewalls, causing the pressure at the base of the granular column to saturate - a phenomenon called the "Janssen effect". This behaviour originates from the heterogeneous force-chain network within the packing, constrained by geometry and friction. Using ferromagnetic grains under an external magnetic field, we recently demonstrated the remote control of this stress redirection, giving rise to a "magnetic Janssen effect". Here, we go further by showing that the apparent mass of granular columns can be precisely controlled by varying the fraction of ferromagnetic grains and their spatial arrangement within the packing. Combining experiments with discrete-element numerical simulations, we uncover a hybrid magnetic Janssen effect: the apparent mass at the base decreases once the fraction of magnetic grains exceeds a critical threshold. This transition corresponds to the percolation of magnetic clusters, which form a system-spanning network capable of channeling forces laterally. Our findings establish a straightforward pathway toward programmable granular materials, in which load distribution can be actively tuned using external fields.

Density-driven convection enhances the carbon dissolution rate, which is significant for the geological carbon storage. This process will also influence the spatiotemporal pH and carbon concentrations of the underground fluid. To illuminate the convection mechanism, it is critical to understand the evolution of those properties within the porous media. However, determining the spatiotemporal pH and concentration within porous media is always challenging. This study employed a combination of three pH indicators that can track a wide range in pH from 4 to 9.5 in a convection experiment. Furthermore, we compared three image-processing techniques- Hue, gray-difference, and angular representation of RGB color space (phi, theta)-for quantifying color changes from the universal pH indicator arising from the carbon convection. The characterized colors were mapped into pH by calibrating against benchmark solutions. The comparative results demonstrate that the color quantified by the Hue technique is most robust, showing invariance to fluid thickness, camera settings, and LED luminance. In the convection experiments, it produces a continuous spatial distribution of pH and concentration level in the system. In contrast, the (phi, theta) and gray-difference techniques were more sensitive to environmental variations. They also have significant limitations for pH interpolation in the critical range due to their non-monotonic calibration paths. Although all methods ultimately produced similar estimates of total dissolved carbon, the Hue technique offers greater stability and universality for high-resolution, dynamic measurements of pH and carbon concentration in the convection experiments.

Effective stress in partly saturated porous media is a crucial question to understand the mechanical stability and the erodability of soils. In general, two-phase flow in unconsolidated granular media is a common process. It takes place during rain infiltration in soils, in sandcastles, and numerous situations in the critical zone.The mechanical stability of slopes and materials is expressed by considering stability envelope of the stress tensor supported by the solid material. In one phase flow, this leads to criterias on Terzaghi stress, or effective stress when the contacts between solid elements are not reduced to points.In two-phase flow, the stress carried by solids is usually expressed using an effective average fluid pressure in the effective stress formulation, following Bishop. We show that this approach does not take the explicit stress carried by the two-dimensional interface between the two fluids into account: the explicit effect of surface tension is missing. This term is called Bachelor stress in the framework of foam mechanics, but is usually not incorporated in two-phase flow in porous media formulationWe evaluate the importance of this effect from a micromechanical perspective, and show how to incorporate it in a generalized large scale effective stress formulation. We show how this formulation can take into account an anisotropic tensor reflecting the stress carried by the fluids and the fluid/fluid interfaces, depending on the anisotropy of the fabrics of these interfaces.We bridge the gap between microscopic interactions and macroscopic behavior, offering a robust model for evaluating and predicting forces in multi-phase systems. Numerical simulations comparing the standard model with the new framework demonstrate that incorporating surface tension significantly refines slope stability predictions, especially during intense rainfall events.

In the context of deep reservoir exploitation, it is necessary to enhance reservoir permeability before exploitation. One method to achieve this is by conducting stimulations through fluid injection, which increases pore pressure, reduces the effective normal stress and allows dilatant shear and porosity increase along small fractures in the reservoir, in the vicinity of the injection well. The pore pressure diffuses throughout the reservoir and can also sometimes reach distant faults that are critically stressed, with a risk to trigger seismicity along these. The model we propose aims to decrease the effective normal stress reduction caused by pressure disturbance along such distant faults, which can cause the rupture of critically stressed distant faults and induce seismic activity. This work investigates an alternative pumping method to stimulate a reservoir without triggering distant faults. To achieve this, a numerical model based on the finite difference method has been developed to solve the diffusion equation of pressure disturbances. The simplifying assumption is that the domain is isotropic and homogeneous. The 2D domain represents the fault plane and permeable damaged zone embedded in less permeable rock. To validate the numerical model, the numerical distant pressure disturbances are compared to analytical solutions developed from the Green's function of the diffusion equation. The numerical model investigates the impact of a time-dependent oscillating injection strategy on near-well and distant pressure disturbances, in comparison to other tested methods, to minimize induced seismicity. The results suggest that the oscillating pumping strategy has the potential to significantly reduce induced seismicity on distant faults. Future research will involve developing mitigation strategies using more complex models that incorporate realistic fault geometries and operational conditions.

We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly-packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced fluorescence imaging to resolve the morphology and stability of the moving interface resulting from the injection of one fluid into another. The imposed injection rate sets a balance between gravitational and viscous forces, producing interface morphologies which range from unstable collections of tangled fingers at low rates to stable sheets at high rates. The image data are complemented by time-resolved pressure measurements. We develop a stability criterion for the fluid interface based on the analysis of the 3D images and the pressure data. This criterion involves the Darcy permeability in each of the two phases and the time derivative of the pressure drop across the medium. We observe that the relative permeability encountered by the invading fluid is modified by the imposed flow rate in our experiment, which impacts the two-phase flow dynamics. We show that, in addition to the balance between the relevant forces driving the dynamics, local regions of crystalline order in the beadpack (crystallites) affect the stability of the invading front. This work provides insights into how disorder on multiple length scales in porous media can interact with viscous, capillary, and gravitational forces to determine the stability and dynamics of immiscible fluid interfaces.

A theoretical approach to estimating stable drainage front widths in three-dimensional (3D) random porous media under gravitational and capillary effects is presented here. Based on the frontier of the infinite cluster in gradient percolation, we propose an expression for the 3D front width dependent on the pore-network topology, the distribution of capillary-pressure thresholds for the pore throats, the stabilizing capillary-pressure gradient, the average pore size, and the correlation length critical exponent from percolation in three dimensions. Theoretical predictions are successfully compared to numerical results obtained with a bond invasion-percolation model for a wide range of drainage flow parameters.

Density-driven convection of CO2 in water will trigger the spatiotemporal evolution of pH and carbon concentration, impacting the understanding of CO2 dissolution and implementations of geological carbon sequestration. Building upon the conventional methodology which applies a single pH indicator and Schlieren imaging analysis, the enhanced experimental technique, offering a holistic view of CO2 convection within water, resulted in an accurate and visual representation of the CO2 plume propagation and a wider range of pH alteration and carbon concentration during CO2-water interactions. In response to the broad pH variations with continuous CO2 dissolution, this study utilized three pH indicators combined with the novel image analysis method to correlate the solutions’ colors to their pH. Afterwards, the carbon concentration is derived from the pH values by employing the pseudo-equilibrium theories. Leveraging an experimental technique and analytical tools to measure the spatiotemporal pH and carbon concentration, the research aims to deepen the understanding of CO2 convection behaviors, paving the way for enhanced insights into carbon sequestration and related environmental processes.Keywords: Carbon sequestration, CO2 convection, density-driven, pH, carbon concentration

Measuring the rheology of liquids typically requires precise control over shear rates and stresses. Here, we describe an alternative route for predicting the characteristic features of a power-law fluid by simply observing the capillary spreading dynamics of viscous droplets in a wedge-shaped geometry. In this confined setting, capillary and viscous forces interact to produce a spreading dynamics described by anomalous diffusion, a process where the front position grows as a power-law in time with an exponent that differs from the value 1/2 found in classical diffusion. We derive a nonlinear diffusion equation that captures this behavior, and we show that the diffusion exponent is directly related to the rheological exponent of the fluid. We verify this relationship by using both experiments and simulations for different power-law fluids. As the predictions are independent from flow-specific details, this approach provides a robust tool for inferring rheological properties from the spreading dynamics.

Drainage in porous media can be broken down into two main mechanisms: a primary piston-like displacement of the interfaces through the bulk of pore bodies and throats, and a secondary slow flow through corners and films in the wake of the invasion front. In granular porous media, this secondary drainage mechanism unfolds in connected pathways of pendular structures, such as capillary bridges and liquid rings, formed between liquid clusters. To represent both mechanisms, we proposed a dynamic dual-network model for drainage, considering that a gas displaces a wetting liquid from quasi-2D granular porous media. For this model, dedicated analyses of the capillary bridge shapes and hydraulic conductivity were conducted so that the secondary drainage mechanism could be properly quantified at finite speeds. With the model, an investigation of the wetting-phase connectivity and flow during drainage was carried out, covering a broad range of flow conditions. Results indicate that the span of liquid-connected structures in the unsaturated region, as well as their ability to contribute to flow, varies significantly with Capillary and Bond numbers.

The risk of induced and triggered seismicity is often present in deep geothermal resources exploitation. These facilities allow exploiting practical and green energy resources.There are many regions with high geothermal capacity, such as Alsace, France. In Vendenheim, north of Strasbourg, the Geoven plant project was expected to extract geothermal energy from the Robertsau fault by circulating fluid at depth.Two clusters of humanly perceivable seismicity occurred in 2019-2020, one of them close to wells and other one at the Robertsau area at 5km to the south. A question was raised about a possible link between these seismic events and wells activities of Geoven site. A large distance with no earthquakes between the injection wells and the southern cluster was reason for disagreement between scientific experts and the company in charge about the link between the injection and the seismicity on this cluster.Our objective is studying such a possible connection with numerical modeling through a simple methodology based on fluid/solid deformation and mechanical coupling. In addition, we aim at modelling the pressure perturbation during the time resulting from the history of the injection flux and comparing it with measured data.The methodology has 3 steps: 1. Structural plan: extracting the geometry of the fault and tectonic stresses 2. Mechanical stability: the stresses on the fault are evaluated and the risk of earthquake triggering is analyzed based on Mohr-Coulomb criterion. 3. Pore Pressure: a quasi 2D pressure diffusion equation with the proper injection parameters is solved for modeling pressure perturbation in the area due to water injection/extraction.According to the results, the fault is strong enough in the northern cluster area and slip can happen only by high activation pressure. However, slip and micro-earthquakes resulted from large pressure increase near the wells, which is necessary for permeability increase to improve the transmissivity of the reservoir. On the other hand, the fault is in the weakest state around the southern cluster, because the pressure required for sliding drops sharply. Indeed, with low amount of pressure increase, slip occurs. Our simulation shows that, the triggered earthquake is expected at this point, due to large enough pressure increase. But between these two clusters, not only is the fault resistant based on its orientation, but also the pore pressure increase is notlarge enough for slip. This explains, the distance of 5km between the two clusters, and absence of earthquakes in between.Also, we simulated the pressure perturbation in the wells resulting from real injection regime data, during 85 days of operation in Geoven site in 2020, and compare it with real pressure change.In conclusion, the lowest activation pressure in comparison to other parts can be observed around the southern cluster, which is coherent with the fault and stress tensor geometry implying a weak state in this location. Also, we identify a physical mechanism showing that earthquakes in that zone were possibly triggered by pore pressure perturbation resulting from the Geoven operation.

Rainfall-induced landslides (RILS) are commonly investigated using hydro-mechanical models with the concept of local factor of safety. The inputs of these models are usually prone to uncertainties. An uncertainty analysis is required to investigate how uncertainties propagate through the model and impact the predictions. An appropriate strategy for uncertainty propagation analysis is suggested in this work to deal with nonlinearity and high dimensionality of RILS problems. It proceeds by performing a sensitivity analysis in two steps. A screening technique is first applied to eliminate insignificant parameters. Then, a global sensitivity analysis is performed to rank the parameters by order of importance. The Sobol indices are used as sensitivity metrics. The polynomial chaos expansion is used to compute the Sobol indices. The proposed strategy is first applied to a hypothetical benchmark and then to a more realistic configuration where prior knowledge of parameters and type of soil are considered. The results show that, when prior knowledge of soil is available, the most important parameters are the coefficient of cohesion, friction angle and air entry pressure head, respectively. The results also show that 10% uncertainty on these parameters leads to about 20% uncertainty on the prediction of slope stability.

A striking viscous fingering fractal pattern arises when a less-viscous fluid displaces a more-viscous fluid from a quasi-2D porous network [1]. On the left we show an experimental image of the process and on the right a digitally colored reconstruction, where the colors map the invasion time (blue for the start of the experiment and red for the end). The experiment is performed by the fast injection of air into a glycerol-water mixture that initially saturates a quasi-2D porous medium. The medium is composed by a monolayer of glass beads (diameter 1mm) placed in the gap of a modified Hele-Shaw cell. The air injection rate was 35 ml/h.

The drying of a granular-liquid mixture in a Hele-Shaw cell leaves behind a labyrinth residue[1]. In the picture, the golden walls are glass beads, bulldozed aside by invading ngers of air (black) carving out paths in the granular layer.

Frictional fluid dynamics describes the displacement patterns that arise when a confined mixture of liquid and grains are displaced by an immiscible fluid under pressures that are too small to cause drainage into single pores. The flow, which is governed by solid friction and capillary forces, thus bulldozes the grains into compaction fronts which give rise to propagating fingers that eventually interact to create a range of patterns, including labyrinthine ones. We derive an analytic description that successfully reproduces the experimental results for the shape of a single finger as well as the compaction front profile. The theory thus depends on only one fitting parameter.

Numerous natural and industrial processes involve the mixed displacement of liquids, gases and granular materials through confining structures. However, understanding such three-phase flows remains a formidable challenge, despite their tremendous economic and environmental impact. To unveil the complex interplay of capillary and granular stresses in such flows, we consider here a model configuration where a frictional fluid (an immersed sedimented granular layer) is slowly drained out of a horizontal capillary. Analyzing how liquid/air menisci displace particles from such granular beds, we reveal various drainage patterns, notably the periodic formation of dunes, analogous to road washboard instability. Considering the competitive role of friction and capillarity, a 2D theoretical approach supported by numerical simulations of a meniscus bulldozing a front of particles provides quantitative criteria for the emergence of those dunes. A key element is the strong increase of the frictional forces, as the bulldozed particles accumulate and bend the meniscus horizontally. Interestingly, this frictional enhancement with the attack angle is also crucial in small-legged animals' locomotion over granular media.

Liquid-filled corners and capillary bridges can establish networks connecting seemingly isolated clusters during drainage in porous media. Coupled with drainage through the bulk of pores and throats, the flow through these networks constitutes a secondary drainage mechanism that can significantly affect fluid configurations and residual saturations. In order to investigate the prevalence of this drainage mechanism, we propose a quasi-static pore-network model based on modifying the trapped-cluster-identification algorithm in an invasion-percolation model. With the modification, wetting-phase connectivity is provided by direct successions of pores and throats, represented by sites and bonds, as well as by chains of interconnected capillary bridges. The advancement of the fluid interface in the porous matrix is determined by the bonds’ invasion thresholds and local capillary pressure values, calculated taking into consideration gravitational effects. With the proposed model, experimentally verified phenomena related to slow drainage in granular porous media are reproduced, showing good qualitative agreement.

Experimental method: development of an optical 3D scanner based on index matching. First trial experiment of the working 3Dscanner. We see inside a cell filled with 3 mm glass beads. The cell is illuminated by a laser sheet parallel to the imaging plane. The green defending fluid, glycerol, is illuminated by green fluorescence (Fluorescein 549), in red, coming in from below, we see the invading fluid, canola oil, dyed with red (Pyrromethene 650).

Soils that seem dry can contain vast amounts of water trapped under the surface.

Multiphase flows involving granular materials are complex and prone to pattern formation caused by competing mechanical and hydrodynamic interactions. Here we study the interplay between granular bulldozing and the stabilising effect of viscous pressure gradients in the invading fluid. Injection of aqueous solutions into layers of dry, hydrophobic grains represent a viscously stable scenario where we observe a transition from growth of a single frictional finger to simultaneous growth of multiple fingers as viscous forces are increased. The pattern is made more compact by the internal viscous pressure gradient, ultimately resulting in a fully stabilised front of frictional fingers advancing as a radial spoke pattern.