When a less viscous fluid displaces a more viscous one in a porous medium, the interface becomes unstable, forming viscous fingers. While viscous fingering has been studied in depth, previous work has focused on the pre-breakthrough dynamics – that is, before the injected fluid reaches any outlet boundary. Here, we investigate post-breakthrough behaviour in a radial micromodel through experiments and pore-network simulations. Post-breakthrough displacement is key for practical applications, as it governs how much of the defending fluid is ultimately recovered. We show that the displacement pattern either ‘freezes’ or continues to grow, depending on the capillary number italic Ca Ca $ \textit{Ca}$ and viscosity ratio upper M M $M$ . A pore-network model predicts a sharp drop in growth rate at breakthrough and a geometry-controlled cross-over italic Ca Subscript times Ca × $ \textit{Ca}_\times$ below which the displacement pattern is arrested. These results highlight the role of domain size, pore geometry, fluid properties and injection rate in regulating the post-breakthrough dynamics and provide a framework for optimising displacement efficiency.

The displacement of a more viscous fluid by a less viscous immiscible fluid in confined geometries is a fundamental problem in multiphase flows. Recent experiments have shown that such fluid-fluid displacement in micro-capillary tubes can lead to interfacial instabilities and, eventually bubble pinch-off. A critical yet often overlooked aspect of this system is the effect of tube's deformability on the onset of interfacial instability and bubble pinch-off. Here, we present a computational fluid-structure interaction model and an algorithm to simulate this fluid-fluid displacement problem in a soft capillary tube. We use a phase-field model for the fluids and a nonlinear hyperelastic model for the solid. Our fluid-structure interaction formulation uses a boundary-fitted approach and we use Isogeometric Analysis for the spatial discretization. Using this computational framework, we study the effects of inlet capillary number and the tube stiffness on the control of interfacial instabilities in a soft capillary tube for both imbibition and drainage. We find that the tube compliance delays or even suppresses the interfacial instability and bubble pinch-off- a finding that has important implications for flow in soft porous media, bio-microfluidics, and manufacturing processes.

This study investigates the impact of fault permeability anisotropy on the nucleation and rupture of injection-induced earthquakes. Using numerical models, we analyze the effects of varying fault permeability in both, transverse and longitudinal directions. Our research focuses on understanding how these hydraulic properties influence the onset of slip, the nucleation length, and the propagation of the rupture. We simulate more than 400 cases with different combinations of friction parameters and hydraulic properties, verifying that the reference scaling L infinity = b G ' Dc n provides satisfactory results for scaling (b-a)2 o ' nucleation length. Our findings indicate that increased fault permeability delays the onset of slip and affects nucleation patterns, with high longitudinal permeability promoting larger nucleation lengths and high transverse permeability resulting in longer nucleation times. During rupture propagation, poroelastic effects cause undrained responses in pore pressure, significantly affecting the fault strength. Permeable faults exhibit more symmetrical rupture patterns and higher seismic moments than impermeable faults. The study highlights the crucial role of hydraulic properties in the development of nucleation and rupture of induced earthquakes, emphasizing the importance of these properties for designing safer injection protocols.

Accurate prediction and parameter identification of multiphase flow in porous media remain central challenges in geological carbon dioxide storage due to strong nonlinearities, high-dimensional parameter spaces, and limited observational data. We present a machine learning framework that integrates surrogate modeling and Bayesian inference to enable efficient forward prediction and inverse parameter estimation for CO2-brine flows in geological media. The approach is demonstrated using the "FluidFlower" experimental rig, a controlled laboratory system that provides high-resolution, time-resolved observations of CO2 migration in heterogeneous porous media. A convolutional neural network surrogate is trained on high-fidelity numerical simulations to learn the evolution of CO2 saturation and dissolved CO2 concentration fields over a wide range of multiphase flow properties. The trained surrogate is embedded within a Markov chain Monte Carlo framework for parameter inference conditioned on experimental observations. Results show that the surrogate accurately captures large-scale CO2 plume migration, dissolution dynamics, and multiphase flow behavior while providing orders-of-magnitude acceleration compared to traditional simulations. Embedding the surrogate within a Bayesian framework enables computationally tractable exploration of the parameter space and reveals both identifiable and non-identifiable parameter combinations that produce similar plume behavior. By leveraging spatially and temporally resolved full-field observations, the framework substantially improves agreement between simulations and experiments compared to previous manual calibrations based on limited plume-scale metrics. Analysis using progressively increasing observation horizons further shows that observations become more informative once the plume interacts with geological features such as faults and sealing layers.

Nearly a century of oil production in the Wilmington Oil Field, Los Angeles Basin, California, has modified the stress state, caused nearly 9 m of ground surface subsidence, and been associated with earthquakes that sheared wells. This offers a unique opportunity to elucidate the processes that govern these phenomena: Since the 1930s, approximately 2.5 billion barrels of oil have been produced, accompanied by water injection volumes roughly an order of magnitude larger. Combined with extensive structural and geophysical constraints, this history allows us to interrogate the long-term geomechanical impacts of reservoir operations. Here, we assess (i) how the initial stress state, typically uncertain in the shallow crust (<5 km depth), influences subsidence and uplift, and (ii) how production and injection operations affect fault stability. Our numerical model, calibrated with published measurements of reservoir pressures and surface displacements, incorporates a detailed representation of fault surfaces within and around the field, well-level production and injection schedules, and an elastoplastic constitutive framework. Model results show that the previously assumed stress regime in the field (reverse faulting) needs to be reassessedx2014the best match to the ground deformation data is achieved when the sedimentary section is initialized with low deviatoric stress (i.e., not critically stressed). This suggests significant variation in the stress state with depth, including a likely change in the stress regime. DCFF values suggest minor destabilization on reservoir faults and larger changes on sub-horizontal bedding planes; both could explain the faulting that led to sheared wells and seismicity between 1947 and 1961.

Fault zones exhibit complex and heterogeneous permeability structures influenced by stratigraphic, compositional, and structural factors, making them critical yet uncertain components in subsurface flow modeling. In this study, we investigate how lithological controls influence fault permeability using the PREDICT framework: a probabilistic workflow that couples stochastic fault geometry generation, physically constrained material placement, and flow-based upscaling. The flow-based upscaling step, however, is a very computationally expensive component of the workflow and presents a major bottleneck that makes global sensitivity analysis (GSA) intractable, as it requires millions of model evaluations. To overcome this challenge, we develop a neural network surrogate to emulate the flow-based upscaling step. This surrogate model dramatically reduces the computational cost while maintaining high accuracy, thereby making GSA feasible. The surrogate-model-enabled GSA reveals new insights into the effects of lithological controls on fault permeability. In addition to identifying dominant parameters and negligible ones, the analysis uncovers significant nonlinear interactions between parameters that cannot be captured by traditional local sensitivity methods.

We study the mobilization of an oil droplet in a deformable, actuated constricted tube subjected to two different actuation mechanisms: hydrodynamic actuation (oscillatory body force in the fluid) and dynamic wall actuation (oscillatory traction on the tube walls). Using high-resolution fluid-structure interaction simulations, we analyze the effects of actuation frequency and amplitude on droplet transport through the constriction. Our simulations show that hydrodynamic actuation leads to a monotonic increase in the droplet's mobilization time with increasing actuation frequency, and a decrease with increasing actuation amplitude. In contrast, dynamic wall actuation exhibits a resonance effect-the mobilization time reaches a minimum at a frequency near the tube's resonant frequency. Our study highlights the potential of actuation mechanisms in deformable tubes for precise control of droplet transport in bio-microfluidic applications.

Supershear earthquakes are a particular class of seismic events in which the rupture velocity exceeds the shear wave velocity. These high-speed ruptures challenge conventional fault mechanics and have significant implications for the assessment of seismic hazards. This work investigates the relationship between pore pressure-dependent friction laws and the propagation of seismic ruptures, particularly the transition to supershear speeds. We present a numerical approach that couples fluid flow, rock deformation, and frictional contact, using stress-rate-dependent rate-and-state friction laws to simulate fault reactivation and rupture propagation. Our simulations demonstrate that the dependence of frictional properties on the effective normal stress rate can partially explain the occurrence of supershear ruptures, leading to a transition from sub-Rayleigh to supershear propagation patterns, as opposed to classical rate-and-state laws. We perform a parametric sweep, varying confining stresses, tectonic ratio, and fluid compressibility, and perform a dimensionless analysis to quantify the impact of hydromechanical parameters on supershear ruptures. Our analysis reveals that the stress drop during rupture is a key parameter in distinguishing between sub-Rayleigh and supershear rupture regimes. This study contributes to understanding the mechanisms that control fault friction behavior and its impact on seismic risk in underground reservoirs, which is crucial for the safe implementation of technologies such as green hydrogen storage and geothermal energy.

Recent studies indicate that Miocene-age reservoirs offshore Texas are promising candidates for industrial-scale geologic carbon sequestration. Fault-bounded hydrocarbon traps are common, and faults may be less competent seals than the low-permeability sediments overlying the reservoirs; this means that faults may limit the amount of CO(2)that can be permanently sequestered. Here, we conduct flow simulations of megatonne-scale CO(2)injection next to a major, reservoir-bounding growth fault, and evaluate (a) where fault sealing capacity is exceeded, and (b) where the CO(2)migrates after it enters the fault zone. We use a geologic model that includes the key structural features of fault-bounded systems near-offshore Texas, and consider both homogeneous and layered top seals (TSs). To model fault petrophysics, we apply a new, general methodology for faults in normally-consolidated, relatively shallow (depth < similar to 3 km) sequences that populates three-dimensional realizations of the fault core with sand and clay smears. We quantify uncertainty in the directional components of the fault permeability tensor and multiphase flow fault properties. We evaluate the sensitivity of fault CO(2)migration to these properties, and show that the capillary entry pressure is exceeded in the lower portion of the fault. This leads to fault CO(2)migration being controlled by effective fault permeability. For the cases considered, the amount of CO(2)remaining in the injection formation after 1,000 years exceeds 93%, and CO(2)does not migrate to depths shallower than the TS. These results suggest that, in the Miocene section, faults partially offsetting the TS do not act as preferential CO(2)conduits.

Stick-slip on preexisting faults has long been associated with velocity-dependent and time-dependent friction. The description, however, has not adequately addressed position-dependent friction, an aspect that is relevant to spatially complex fault zones in nature. Here we show how the interaction between irregular surfaces results in heterogeneous Coulomb friction along the interface. We then conduct dynamic simulations of a spring-slider model and find that heterogeneity in Coulomb friction alone is capable of reproducing a wide range of stick-slip phenomena that may be associated with complex fault slip behaviors, from fault creep and low frequency earthquakes to ordinary earthquakes and slow slip events.

Abstract Geologic CO2 storage is an important strategy for reducing greenhouse gas emissions to the atmosphere and mitigating climate change. In this process, coupling between mechanical deformation and fluid flow in fault zones is a key determinant of fault instability, induced seismicity, and CO2 leakage. Using a recently developed methodology, PREDICT, we obtain probability distributions of the permeability tensor in faults from the stochastic placement of clay smears that accounts for geologic uncertainty. We build a comprehensive set of fault permeability scenarios from PREDICT and investigate the effects of uncertainties from the fault zone internal structure and composition on forecasts of CO2 permanence and fault stability. To tackle the prohibitively expensive computational cost of the large number of simulations required to quantify uncertainty, we develop a deep‐learning‐based surrogate model capable of predicting flow migration, pressure buildup, and geomechanical responses in CO2 storage operations. We also compare our probabilistic estimation of CO2 leakage and fault instability with previous studies based on deterministic estimates of fault permeability. The results highlight the importance of including uncertainty and anisotropy in modeling of complex fault structures and improved management of geologic CO2 storage projects.

We present a phase-field model to study two-phase displacement with moving contact lines in a capillary tube. We construct a diffuse-interface formulation of solid-liquid surface energy by enforcing a consistent structure of the fluid-fluid interface between the bulk fluid and the solid surface. We first show, via simulation of equilibrium liquid slugs in a capillary tube, that this formulation allows prescribing arbitrary static contact angles and leads to the correct capillary pressure. We then propose a formulation to account for out-of-equilibrium dynamics near the contact line and demonstrate the ability of this generalized formulation to simulate spontaneous imbibition as well as viscously unstable, constant-rate displacements in a capillary tube. We show that our phase-field model captures the imbibition dynamics described by a theoretical model that combines classic Lucas-Washburn theory with Cox's law of dynamic contact angle. It also predicts wetting transition, thin-film formation, and interface pinch-off that quantitatively agree with recent experiments.

In this work, we introduce a novel neural operator, the Solute Transport Operator Network (STONet), to efficiently model contaminant transport in micro-cracked porous media. STONet's model architecture is specifically designed for this problem and uniquely integrates an enriched DeepONet structure with a transformer-based multi-head attention mechanism, enhancing performance without incurring additional computational overhead compared to existing neural operators. The model combines different networks to encode heterogeneous properties effectively and predict the rate of change of the concentration field to accurately model the transport process. The training data is obtained using finite element (FEM) simulations by random sampling of micro-fracture distributions and applied pressure boundary conditions, which capture diverse scenarios of fracture densities, orientations, apertures, lengths, and balance of pressure-driven to density-driven flow. Our numerical experiments demonstrate that, once trained, STONet achieves accurate predictions, with relative errors typically below 1% compared with FEM simulations while reducing runtime by approximately two orders of magnitude. This type of computational efficiency facilitates building digital twins for rapid assessment of subsurface contamination risks and optimization of environmental remediation strategies. The data and code for the paper are accessible at https://github.com/ehsanhaghighat/STONet.

This study evaluates the viability of single-well spherical-cylinder salt caverns (SWCSs) for green hydrogen storage in bedded salt formations. Using numerical simulations, we demonstrate their ability to store significant volumes of energy, up to hundreds of GWh. SWCSs, designed with a single vertical well to avoid the horizontal drilling and multi-step dilution processes, provide a structurally viable and cost-effective alternative to two- well horizontal caverns (TWHs). These caverns take advantage of the horizontal dimensions of the bedded formations within their vertical constraints. Given the expanding role of hydrogen in global energy systems, the adoption of SWCSs can enhance the storage capacity and operational flexibility of systems associated with the hydrogen economy. Future studies should validate these findings experimentally to promote the implementation of SWCSs.

Geologic CO$_2$ storage is an important strategy for reducing greenhouse gas emissions to the atmosphere and mitigating climate change. In this process, coupling between mechanical deformation and fluid flow in fault zones is a key determinant of fault instability, induced seismicity, and CO$_2$ leakage. Using a recently developed methodology, PREDICT, we obtain probability distributions of the permeability tensor in faults from the stochastic placement of clay smears that accounts for geologic uncertainty. We build a comprehensive set of fault permeability scenarios from PREDICT and investigate the effects of uncertainties from the fault zone internal structure and composition on forecasts of CO$_2$ permanence and fault stability. To tackle the prohibitively expensive computational cost of the large number of simulations required to quantify uncertainty, we develop a deep-learning-based surrogate model capable of predicting flow migration, pressure buildup, and geomechanical responses in CO$_2$ storage operations. We also compare our probabilistic estimation of CO$_2$ leakage and fault instability with previous studies based on deterministic estimates of fault permeability. The results highlight the importance of including uncertainty and anisotropy in modeling of complex fault structures and improved management of geologic CO$_2$ storage projects.

Abstract Characterization of induced microseismicity at a carbon dioxide (CO2) storage site is critical for preserving reservoir integrity and mitigating seismic hazards. We apply a multilevel machine learning (ML) approach that combines the nonnegative matrix factorization and hidden Markov model to extract spectral representations of microseismic events and cluster them to identify seismic patterns at the Illinois Basin‐Decatur Project. Unlike traditional waveform correlation methods, this approach leverages spectral characteristics of first arrivals to improve event classification and detect previously undetected planes of weakness. By integrating ML‐based clustering with focal mechanism analysis, we resolve small‐scale fault structures that are below the detection limits of conventional seismic imaging. Our findings reveal temporal bursts of microseismicity associated with brittle failure, providing insights into the spatio‐temporal evolution of fault reactivation during CO2 injection. This approach enhances seismic monitoring capabilities at CO2 injection sites by improving fault characterization beyond the resolution of standard geophysical surveys.

Recent studies indicate that Miocene‐age reservoirs offshore Texas are promising candidates for industrial‐scale geologic carbon sequestration. Fault‐bounded hydrocarbon traps are common, and faults may be less competent seals than the low‐permeability sediments overlying the reservoirs; this means that faults may limit the amount of that can be permanently sequestered. Here, we conduct flow simulations of megatonne‐scale injection next to a major, reservoir‐bounding growth fault, and evaluate (a) where fault sealing capacity is exceeded, and (b) where the migrates after it enters the fault zone. We use a geologic model that includes the key structural features of fault‐bounded systems near‐offshore Texas, and consider both homogeneous and layered top seals (TSs). To model fault petrophysics, we apply a new, general methodology for faults in normally‐consolidated, relatively shallow (depth km) sequences that populates three‐dimensional realizations of the fault core with sand and clay smears. We quantify uncertainty in the directional components of the fault permeability tensor and multiphase flow fault properties. We evaluate the sensitivity of fault migration to these properties, and show that the capillary entry pressure is exceeded in the lower portion of the fault. This leads to fault migration being controlled by effective fault permeability. For the cases considered, the amount of remaining in the injection formation after 1,000 years exceeds 93%, and does not migrate to depths shallower than the TS. These results suggest that, in the Miocene section, faults partially offsetting the TS do not act as preferential conduits.

We perform a direct comparison between experiment and simulation of density-driven convective mixing in three-dimensional (3D) porous media. We find excellent agreement between the experiment and the model in terms of both the convection fingering pattern and the average rate of fluid mixing. In particular, the experiment exhibits dynamic self-organization of columnar plumes into a reticular pattern, which, until now, had only been observed in 3D simulations. We also report good quantitative agreement between the experiment and simulation in the evolution of the state of mixing by comparing, over time, (i) the average concentration at depth, (ii) the variance of the concentration field, (iii) the scalar dissipation rate, and (iv) the dissolution flux. We derive a relation between the scalar dissipation rate and the dissolution flux in a closed system, and we show that the flux in a 3D system is approximately similar to 30% higher than in a 2D system, confirming previous numerical estimates.

Geological storage of carbon dioxide is a cornerstone in almost every realistic emissions reduction scenario outlined by the Intergovernmental Panel on Climate Change. Our ability to accurately forecast storage efficacy is, however, mostly unknown due to the long timescales involved (hundreds to thousands of years). To study perceived forecast accuracy, we designed a double-blind forecasting study. As ground truth, we constructed a laboratory-scale carbon storage operation, retaining the essential physical processes active on the field scale, within a time span of five days. Separately, academic groups with experience in carbon storage research were invited to forecast key carbon storage efficacy metrics. The participating groups submitted forecasts in two stages: First independently without any cross-group interaction, then finally after workshops designed to share and assimilate understanding between the forecast groups. Their confidence in reported forecasts was monitored throughout the forecasting study. Our results show that participating groups provided forecasts that appear biasfree with respect to carbon storage as a technology, yet the forecast intervals are too narrow to capture the ground truth (overconfidence bias). When asked to qualitatively self-assess their forecast uncertainty (and later when asked to provide an external assessment of other forecast groups), the assessment of the participants indicated an understanding that the forecast intervals (both their own and those of others) were too narrow. However, the participants did not display an understanding of how poorly the forecast intervals calibrated to the ground truth. The quantitative uncertainty assessments contrast the qualitative comments supplied by the participants, which indicate an acute awareness of the challenges associated with assessing the uncertainty of forecasts for complex systems such as the geological storage of carbon dioxide.

In this paper, a novel methodology to improve the structural behaviour and durability of bedded salt caverns for hydrogen storage is proposed. The suggested technology consists in applying a gunite lining over the whole cavern surface by means of a pneumatic air blowing. This continuous flow projected at high speed onto the cavern surface produces a self-compacted gunite facing. The effect of adding a gunite lining on the structural performance of a bedded salt cavern is analysed. The nonlinear finite element method is then applied to solve the inherent nonlinear solid mechanics problem. It is shown that reinforcing salt caverns with a gunite lining improves the cavern behaviour, specially in the case of caverns located within a horizontal salt stratum confined between other strata. When dealing with these salt formations, the stratum geometry limits the cavern height. In general, wider caverns that exhibit larger displacements are required to achieve a huge storage capacity. Moreover, these caverns can be located at a considerable depth, where the temperature has an important role on the creep deformation process. Therefore, the proposition of stabilization techniques is required to ensure both their structural integrity and the ground subsidence. This technology allows the safe exploitation of salt caverns located at bedded-type stratified horizontal salt formations.