Induced calcite precipitation, where CaCO₃ closes voids inside porous media and unconsolidated samples are solidified, is an important technique in geotechnical engineering. To optimize these applications, it is crucial to understand how the dynamics of mineral precipitation affect flow and transport in porous media. The aim of this study is to investigate how different injection strategies affect the spatial and temporal development of calcite precipitation using time-lapse non-invasive imaging with magnetic resonance imaging (MRI) and X-ray microcomputed tomography (µXRCT). These two imaging methods are complementary because µXRCT aims to detect structural changes of the solid matrix, whereas MRI focuses on the liquid phase in the pore space. Together, these methods enable time-resolved observations of the three-dimensional development of porosity, and thus have the potential to offer valuable insights into the spatial and temporal dynamics of the precipitation process.

We performed two distinct types of experiments to induce precipitation by simultaneous injection of a cementing solution consisting of 0.5 M CaCl₂ and 0.5 M urea and an enzyme solution containing 5.0 g/l of Jack Bean meal into homogeneous sand packings prepared in 30 mm long sample cuvettes with a diameter of 15 mm. Two injection strategies were realized. In a first experiment, a constant flow rate of 0.01 mL/s was maintained during six injection cycles. Pressure development was monitored in parallel. In a second experiment, the solutions were injected  at a constant pressure that was increased stepwise during six cycles from initially 50 mbar to 300 mbar to maintain moderate flow rates. Following each cycle, both samples were imaged using XRCT and MRI and the intrinsic permeability was determined.

Imaging results indicate that calcite preciptation occured more strongly close to the inlet, as manifested by water content and relaxation maps from MRI and density maps from XRCT. Only during the last two injection cycles, zones with increased precipitation became visible in the center of the column. The MRI relaxation maps suggest a reduction in pore size due to precipitation, which agreed with increased surface-to-volume ratio of the pores. Vertical porosity profiles derived from XRCT showed an average change of 12 and 11 vol.% for the constant flow and constant pressure inection strategies, respectively, and confirmed the non-uniform distribution observed with MRI. The permeability decreased by two orders of magnitude for both injection strategies. However, this decrease was achieved already after 90 injected pore volumes in case of the constant pressure injection strategy, whereas the constant flow strategy required 165 pore volumes for a comparable decrease. This is attributed to the increased tendency for preferential flow in case of the constant-rate injection strategy, but this needs to be confirmed through a detailed analysis of the variability of calcite precipation within the sample cross-section. Overall, this study showed the feasibility of monitoring induced calcite precipitation using both MRI and XRCT.

How to cite: Emadi, S., Bakhshi, P., Pohlmeier, A., and Huisman, J. A.: Non-invasive imaging of the effect of injection strategy on the spatial and temporal development of enzymatically-induced calcite precipitation, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-7028, https://doi.org/10.5194/egusphere-egu25-7028, 2025.

Fluid/chemical transport in the connected pore network of porous sandstone with variable permeability governs numerous subsurface energetic, environmental, and industrial activities. In this work, we compile a multi-scale pore connectivity evaluation by integrated pore structure characterization involving casting thin section, scanning electron microscope, nuclear magnetic resonance, X-ray computed tomography, and mercury intrusion porosimetries. The pore connected pattern, connective ratio, and connected full-range pore size distribution (CPSD) are obtained by the determination of full-range pore size distribution and empirical correlations between pore size and connective ratio, upon which the across-scale steady-state multiphase flow physics are further explored incorporating physical simulation experiment and numerical analyses. The scale-invariant connective ratio of conventional sandstone with reticular connection pattern stays at around 0.60, that of low-permeability sandstone ranges from 0.53 to 0.60, exhibiting branch-like connection, and it is avg. 0.31 in tight sandstone with local chain-like pattern, of which the ratio can be predicted by its strong dependence on porosity, permeability, and connected median pore radius. With decreasing pore connectivity, the fractional flow of non-wetting phase in steady-state two-phase flow turns from linear deviated flow to power-law flows. The pore-scale interpretations of multiphase mobility and interaction dynamic by incorporating DLVO theory, augmented Young-Laplace equation, and effective hydraulic radius model suggest that the connected full-range pore size distribution determines the wetting phase mobility and non-wetting phase accessibility, controlling the dynamic of multiphase interaction and build of non-wetting phase pathways. Preferential flow path expansions in the connected pores < 1000 nm, leading to strong differences in the resistance for non-wetting phase flow, are the primary reasons for distinctions in flow regimes. The increasing pores of 30-50 nm in the non-wetting phase flow paths are responsible for the TPG, pressure disorders, and fluid snap-offs, resulting in the power-law flow deviations. A dynamic fractional flux prediction model for non-wetting phase is proposed by modifying the fractal-based Hagen-Poiseuille equation considering flow physics, pore heterogeneity, and critical percolation length scale variations along with flow path expansion in the connected pore system. Comparative analysis indicates that the determination of hydraulic flow diameter  should follow the percolation threshold theory and reliable of porous sandstone is at round R₄₀ of the connected flow pathway.

How to cite: Qiao, J., Zeng, J., Jiang, S., and Chen, D.: Pore-scale understandings for steady-state two-phase flow in porous sandstone from full-range pore connectivity quantification, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-15356, https://doi.org/10.5194/egusphere-egu25-15356, 2025.

CO₂ sequestration is a promising method to mitigate anthropogenic CO₂ emissions. When CO₂ is injected into a saline aquifer, its buoyancy leads to the formation of a gravity current that migrates laterally, while CO₂ dissolves into the underlying brine, creating a high-density mixture that can trigger fingering instabilities. In this study, we investigate the migration of this gravity current and the mixing of CO₂ with brine in heterogeneous porous media. Heterogeneity is modeled using horizontally stratified media and multi-Gaussian log-normal permeability fields, characterized by the variance of the log-permeability and its correlation length. We examine how heterogeneity influences the time-evolution of the gravity current and CO₂-brine mixing by analyzing factors such as dissolution fluxes, residual buoyant mass, the length of the CO₂-brine interface, interface width, and mixing volume. Additionally, we explore the impact of different Rayleigh numbers, correlation lengths, and variances on mixing behavior. Our findings aim to enhance the understanding of CO₂ storage in geological formations.

How to cite: Jiménez-Ramos, A., Dentz, M., and Hidalgo, J. J.: Heterogeneity effects on gravity current migration and mixing in porous media, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-11315, https://doi.org/10.5194/egusphere-egu25-11315, 2025.

A hyperbolic description of the problem of solute transport using a deterministic and Lagrangian formulation that combines characteristics of the classical formulations based on the Fokker-Planck (FP) and Langevin equations is developed. This formulation is based on a Liouville master equation, whose hyperbolicity allows for tracing the concentrations along characteristic lines in the augmented phase space composed by solute particle locations and a set of (time-independent) random coefficients used to define a source term that introduces the noise added to the system, in lieu of (time-dependent) stochastic processes. This circumvents the use of stochastic calculus and eliminates the diffusive term of the master equation, at the expense of increasing the dimensionality of the joint probability density function (PDF) of solute particle locations. The characteristic lines define flow maps for the joint PDF and its support such that all one-point space-time statistical information to study mixing and dispersion respectively is contained in them. Therefore, diffusion is modeled with kinematics parametrically dependent on random coefficients. This approach can be combined with numerical algorithms to solve ordinary differential equations (ODEs), that are unaffected by the Courant-Friedrichs-Lewy (CFL) stability condition, do not suffer from Gibbs oscillations, do not require (order-reducing) filtering and regularization techniques, and do not rely on standard Monte Carlo sampling. Because of these reasons this formulation offers more accuracy and a lower computational cost in comparison to Eulerian grid-based and Lagrangian particle tracking solvers. To find the proper noise term to add, we impose that averaging the Liouville equation over the coefficients must lead to the FP equation, which leads to a classical closure problem for the moments of the joint PDF. However, assuming a local linearization in concordance with the Ranz transform used in the lamellae description, a simple closure based on truncated central moments becomes exact and so does this hyperbolic description, which accounts for diffusion in all directions. In this talk, I will discuss the methodological advantages of using a hyperbolic description of mixing, and show how it can be used to construct a numerical lamellae method for arbitrarily shaped initial concentration profiles.

How to cite: Dominguez-Vazquez, D. and Aquino, T.: A numerical lamellae method based on flow maps, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-13723, https://doi.org/10.5194/egusphere-egu25-13723, 2025.

The relative permeability–saturation (k_r–s) relationship is a macroscopic representation of microscale flow characteristics between multiphase immiscible fluids, governed by the interplay among capillary, viscous, and gravitational forces. Previous studies on two phase fluid flow have primarily derived the k_r–s relationship from horizontal core-flooding experiments while neglecting the influence of gravity. However, frequent advent of vertical flows caused by conditions such as macroscale heterogeneity, brine extraction, and CO₂ injection through horizontal well, emphasizes non-negligible gravitational effects varying with the direction of displacement. This study aims to provide experimental evidence of anisotropy on k_r–s relationship induced by gravitational forces, contributing to a deeper understanding of gravity’s role in multiphase flow systems. Steady-state relative permeability tests using a 1-meter acrylic column tightly packed with glass beads and two immiscible fluids were performed under various flow directions. In addition, several total flow rates and beads sizes were used to adjust dimensionless capillary and bond number, which indicate different interplays among three governing forces. Our experiments revealed the differences in the k_r–s relationship between upward and downward flow directions, suggesting that the isotropic k_r–s assumption may not fully capture these dynamics. Under conditions of higher bond number, such as in the finer glass beads, the anisotropy on k_r–s relationship were weaker, indicating the influence of gravitational forces on its anisotropy. This study underscores the need to account for anisotropy on k_r–s relationships under dynamic flow conditions.

Project Acknowledgement

This work was supported by Korea Institute of Energy Technology Evaluation Planning (KETEP) grant funded by the Korea government (MOTIE) (20212010200010, Technical development of enhancing CO2 injection efficiency and increase storage capacity)

How to cite: Lee, C., Ha, S.-W., and Lee, K.-K.: Anisotropy on relative permeability curve under the influence of gravity, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-5358, https://doi.org/10.5194/egusphere-egu25-5358, 2025.

Understanding the probability distributions of flow velocities in heterogeneous porous media is crucial for the study of transport phenomena, as velocity variability controls residence times and dispersion phenomena. However, our knowledge of velocity distributions and their relation to medium structure remains incomplete, especially under partially-saturated conditions, where phase heterogeneity plays a key role in determining the flow structure. In addition, the distributions of shear (the spatial rate of change of velocity transverse to the flow) are essential for understanding the impact of flow on mixing processes, because they represent a key control on solute plume deformation and its interplay with diffusion. Yet, these distributions are far less explored, particularly at the pore scale and under unsaturated conditions. This gap limits our ability to predict the impact of microscopic dynamics on macroscopic plume structure.

In this work, we focus on pore-scale velocity and shear distributions in unsaturated systems. Velocity fields are obtained through numerical simulations based on experimental data for the structure of the medium and fluid-phase distributions. The media are quasi-two-dimensional, with cylindrical pillars of variable radii and different correlation structures, and the flow conditions are such that the spatial phase distributions are time-independent. We characterize velocity and shear distributions and use this information to parameterize Continuous Time Random Walk (CTRW) models to predict solute transport and mixing.

How to cite: Arnal, J., Sole-Mari, G., Borgman, O., Le Borgne, T., and Aquino, T.: Pore-scale shear distributions in unsaturated porous media and their role in transport and mixing, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-6197, https://doi.org/10.5194/egusphere-egu25-6197, 2025.

Geochemical reactions in porous rocks are typically scaled up using effective reaction parameters derived under well-mixed conditions. Such well-mixed conditions are often absent in natural settings. While conventional transport theories based fundamentally on diffusion and dispersion processes can not fully capture the state of mixing, several lines of evidence point to the dominance of chaotic solute mixing. Yet, proving the existence of chaotic mixing in porous rocks remains unresolved mostly due to the limitations in directly observing pore-scale processes. In this work, we present direct evidence of chaotic microscale trajectories in porous rock samples by performing fast high-resolution X-ray tomography at the European Synchrotron Radiation Facility (ESRF). We utilize a custom-designed core holder and highly permeable sandstone and sand pack samples to achieve notably high Peclet numbers during the co-injection of two miscible, highly viscous mixtures of glycerin and brine. These high Peclet numbers are crucial for visualizing chaotic trajectories within the rock pores, as they allow the deformation of fluid fronts to dominate before molecular diffusion blurs the patterns. The existence of such trajectories could significantly enhance microscale concentration gradients, potentially leading to chemical reaction rates that differ from conventional reactive transport model predictions. This difference underscores the need to update kinematic models to incorporate the coupling between chaotic mixing and chemical reactions in porous media for a better understanding and quantification of transport and storage processes in the subsurface.

How to cite: Vafaie, A., Kivi, I. R., Manoorkar, S., Darraj, N. M., Saleh, M., Gomez, F., Lamblin, M., Cordonnier, B., Bihannic, I., Le Borgne, T., Krevor, S., and Heyman, J.: How does imaging help unveil chaotic mixing in porous rocks?, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-9531, https://doi.org/10.5194/egusphere-egu25-9531, 2025.

Displacement of a wetting by a non-wetting fluid in fractured media is a process with relevance for many applications, such as fluid storage in the subsurface or oil and gas exploitation. How to capture the flow in open rough-walled fractures on the large length scales required for such applications is an open question. It is highly questionable if the two-phase flow equations can be simplified to continuum approaches, such as established for porous media, which would allow for coarse spatial resolutions of a model. For this reason, it is necessary to develop a good understanding of how flow regimes and fracture geometry influence the properties of the fluid distributions during a displacement process that determine the macroscopic behavior. Such properties are, for example, fluid that is immobilized behind the displacement front. While there has been extensive investigation of this question in the context of porous media, studies on rough fractures are relatively scarce.

It is well established that in horizontal settings, the displacement is governed by capillary and viscous forces, resulting in the emergence of various displacement patterns (compact, viscous fingering or capillary fingering). Numerical simulations of the flow process could be helpful to relate the flow conditions and geometrical properties of the aperture field to characteristics of fluid distributions. However, such numerical simulations are not straight forward, as capturing the fluid-fluid surfaces and contact lines requires very fine grids and poor representations of the interfaces can cause large numerical errors. It is thus crucial to validate numerical models with well controlled experiments. As it is necessary to have well controlled conditions for boundary conditions and precise knowledge of the geometrical properties of the fracture aperture, such experiments are challenging.

In this contribution, we compare numerical results to recent results from experiments carried out in a setup featuring a fracture flow cell with self-affine rough walled surfaces and a precisely controlled mean aperture. Different viscosity ratios are obtained by altering the viscosities of both the displacing and the displaced fluids and different capillary numbers are obtained by varying the flow rate imposed through the cell. We compare the experimental findings to Direct Numerical Simulation (DNS) results obtained by solving the Navier–Stokes equations within the fracture pore space, employing the Volume of Fluid (VOF) method to track the evolution of the fluid-fluid interface.  We systematically confront the numerical predictions to the experimental results, in terms of various morphological properties of the displacement patterns such as Euler number, cluster size distribution, interfacial length, typical finger width, trapped cluster size distributions or fluid-fluid interface length. From this we infer a range of capillary numbers and viscosity ratios for which the numerical model can be validated as properly predicting the experiments.

How to cite: Neuweiler, I., Krishna, R., Rezaei, A., Borgman, O., Gomez, F., and Méheust, Y.: Drainage in Open Rough-walled Fractures – Comparison of experimental and numerical results, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-20497, https://doi.org/10.5194/egusphere-egu25-20497, 2025.

Low-emission hydrogen accounted for less than 1 % of global hydrogen production by 2023, but will have to increase more than 100-fold by 2030 according to the International Energy Agency’s net-zero emission scenarios for 2050. Proton exchange membrane water electrolyzers are particularly suitable to produce hydrogen from renewable energy sources, yet the currently available technological combinations are considerably more expensive than producing hydrogen from fossil fuels (by 65 % to 810 % according to the International Renewable Energy Agency’s 2021 report). To reduce costs, the materials and dynamic operating conditions in electrolyzers must be optimized, amongst other things with regard to low oxygen concentrations (waste product) at the catalysts. We use a first-principle microscale model for oxygen transport to complement experimental optimization efforts, which are generally expensive and limited by measurement accuracies.

The model deploys the volume of fluid method and accounts for (1) uncertain transport processes in the catalyst layer, (2) numerically challenging two-phase at capillary numbers as low as 2.1 · 10^-7 and (3) bubble detachments in channels. The model is validated with respect to flow patterns in microfluidic experiments as well as to pressure drops and bubble velocities within minichannels (30% and 20% match regarding the latter two). The model is numerically stable at operando conditions with at least 0.5 A/cm² current density in a stochastically reproduced porous transport layer. Uncertain catalyst-side solute transport and nucleations are implicitely accounted for, yet their spatial variations are found to negligibly affect the conditions inside the porous transport layer.  Operando gas saturation measurements are locally matched within a 20% margin and are qualitatively matched across the entire porous transport layer.

The simulated bubble detachment in flow field channels occur at pore throats that agree with porosimetry and microfluidic experiments. The gaseous phase pressure fluctuates greatly according to the detachment throat size and the bubble diameter immediately before detachment. The model allows the prediction of nucleation and detachment sites and can be further utilized to optimize porous transport layers as well as to predict boundary conditions when modeling catalyst layers and flow fields.

How to cite: Schmidt, G. and Neuweiler, I.: Volume of Fluid Modeling of Capillary-Dominated Flow Patterns and Bubble Detachment in PEM Water Electrolyzers , EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-21948, https://doi.org/10.5194/egusphere-egu25-21948, 2025.