We develop a multiscale simulation strategy, namely, algebraic dynamic multilevel (ADM) method, for simulation of fluid flow and heat transfer in fractured geothermal reservoirs under varying thermodynamic conditions. Fractures with varying conductivities are modeled using the projection-based embedded discrete fracture model (pEDFM) in an explicit manner. The developed ADM method allows the fine-scale system to be mapped to a discrete domain with an adaptive grid resolution via the use of the restriction and prolongation operators. The developed framework is used a) to investigate the impacts of formulations with different primary variables on the simulation results, and b) to assess the performance of ADM in a high-enthalpy reservoir by comparing the simulation results against those obtained from fine-scale grids. Results show that the two formulations produce similar results in the case of single-phase flow, which indicates that the molar formulation is a favorable option that can be applied to varying thermodynamic conditions. Moreover, the ADM can provide accurate solutions with only a fraction of fine-scale grids, e.g., for the studied case, the maximum error is by average 1.3 with only 42% of active cells, thereby improving the computational efficiency. This is promising for applying the developed method to field-scale geothermal systems. @en

CO₂ sequestration and storage in deep saline aquifers is a promising technology for mitigating the excessive concentration of the greenhouse gas in the atmosphere. However, accurately predicting the migration of CO₂ plumes requires complex multi-physics-based numerical simulation approaches, which are prohibitively expensive due to highly nonlinear coupled governing equations and uncertainties in heterogeneous spatial parameter distributions. To address this challenge, we developed an end-to-end deep learning workflow employing encoder–decoder architectures with residual network (ResNet) to efficiently predicts the spatial–temporal evolution of the solution CO₂-brine ratio (R_s) and gas saturation (S_g) – the two essential tasks for quantifying the amount of trapped CO₂ – given heterogeneous permeability fields as input. Specifically, we introduce a general multi-task learning with consistency (MTLC) framework to simultaneously predict R_s and S_g. The MTLC model leverages related tasks with less computational expensive labeled datasets to improve generalization ability. In our study, predictions for multiple tasks from the same permeability realization are not independent but expected to be consistent, as the proposed framework utilizes data-driven cross-task consistency constraints to augment learning of related tasks. Our deep learning model is trained based on physical trapping mechanisms, which play a dominant role in the CO₂ migration process. The results demonstrate that the MTLC model with joint learning yields more accurate predictions and improved generalization for predicting CO₂ migration in several test cases. Furthermore, our workflow is 10⁵ times faster than a high-fidelity physics-based numerical simulator, making it a viable alternative for field-scale applications.

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We present an efficient compositional framework for simulation of CO2 storage in saline aquifers with complex geological geometries during a lifelong injection and migration process. To improve the computation efficiency, the general framework considers the essential hydrodynamic physics, including hysteresis, dissolution and capillarity, by means of parameterized space. The parameterization method translates physical models into parameterized spaces during an offline stage before simulation starts. Among them, the hysteresis behavior of constitutive relations is captured by the surfaces created from bounding and scanning curves, on which relative permeability and capillarity pressure are determined directly with a pair of saturation and turning point values. The new development also allows for simulation of realistic reservoir models with complex geological features. The numerical framework is validated by comparing simulation results obtained from the Cartesian-box and the converted corner-point grids of the same geometry, and it is applied to a field-scale reservoir eventually. For the benchmark problem, the CO2 is injected into a layered formation. Key processes such as accumulation of CO2 under capillarity barriers, gas breakthrough and dissolution, are well captured and agree with the results reported in literature. The roles of various physical effects and their interactions in CO2 trapping are investigated in a realistic reservoir model using the corner-point grid. It is found that dissolution of CO2 in brine occurs when CO2 and brine are in contact. The effect of residual saturation and hysteresis behavior can be captured by the proposed scanning curve surface in a robust way. The existence of capillarity causes less sharp CO2-brine interfaces by enhancing the imbibition of the brine behind the CO2 plume, which also increases the residual trapping. Moreover, the time-dependent characteristics of the trapping amount reveals the different time scales on which various trapping mechanisms (dissolution and residual) operate and the interplay. The novelty of the development is that essential physics for CO2 trapping are considered by the means of parameterized space. As it is implemented on corner-point grid geometries, it casts a promising approach to predict the migration of CO2 plume, and to assess the amount of CO2 trapped by different trapping mechanisms in realistic field-scale reservoirs.

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Successful deployment of geological carbon storage (GCS) requires an extensive use of reservoir simulators for screening, ranking and optimization of storage sites. However, the time scales of GCS are such that no sufficient long-term data is available yet to validate the simulators against. As a consequence, there is currently no solid basis for assessing the quality with which the dynamics of large-scale GCS operations can be forecasted. To meet this knowledge gap, we have conducted a major GCS validation benchmark study. To achieve reasonable time scales, a laboratory-size geological storage formation was constructed (the “FluidFlower”), forming the basis for both the experimental and computational work. A validation experiment consisting of repeated GCS operations was conducted in the FluidFlower, providing what we define as the true physical dynamics for this system. Nine different research groups from around the world provided forecasts, both individually and collaboratively, based on a detailed physical and petrophysical characterization of the FluidFlower sands. The major contribution of this paper is a report and discussion of the results of the validation benchmark study, complemented by a description of the benchmarking process and the participating computational models. The forecasts from the participating groups are compared to each other and to the experimental data by means of various indicative qualitative and quantitative measures. By this, we provide a detailed assessment of the capabilities of reservoir simulators and their users to capture both the injection and post-injection dynamics of the GCS operations.

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An efficient compositional framework is developed for simulation of CO ₂ storage in saline aquifers during a full-cycle injection, migration and post-migration processes. Essential trapping mechanisms, including structural, dissolution, and residual trapping, which operate at different time scales, are accurately captured in the presented unified framework. In particular, a parameterization method is proposed to efficiently describe the relevant physical processes. The proposed framework is validated by comparing the dynamics of gravity-induced convective transport with that reported in the literature. Results show good agreement for both the characteristics of descending fingers and the associated dissolution rate. The developed simulator is then applied to study the FluidFlower benchmark model. An experimental setup with heterogeneous geological layers is discretized into a two-dimensional computational domain where numerical simulation is performed. Impacts of hysteresis and the diffusion of CO ₂ in liquid phase on the migration and trapping of CO ₂ plume are investigated. Inclusion of the hysteresis effect does not affect plume migration in this benchmark model, whereas diffusion plays an important role in promoting convective mixing. This work casts a promising approach to predict the migration of the CO ₂ plume, and to assess the amount of trapping from different mechanisms for long-term CO ₂ storage.

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Natural or induced fractures are typically present in subsurface geological formations. Therefore, they need to be carefully studied for reliable estimation of the long-term carbon dioxide storage. Instinctively, flow-conductive fractures may undermine storage security as they increase the risk of CO2 leakage if they intersect the CO2 plume. In addition, fractures may act as flow barriers, causing significant pressure gradients over relatively small regions near fractures. Nevertheless, despite their high sensitivities, the impact of fractures on the full-cycle storage process has not been fully quantified and understood. In this study, a numerical model is developed and applied to analyze the role of discrete fractures on the flow and transport mechanism of CO2 plumes in simple and complex fracture geometries. A unified framework is developed to model the essential hydrogeological trapping mechanisms. Importantly, the projection-based embedded discrete fracture model is incorporated into the framework to describe fractures with varying conductivities. Impacts of fracture location, inclination angle, and fracture-matrix permeability ratio are systemically studied for a single fracture system. Moreover, the interplay between viscous and gravity forces in such fractured systems is analyzed. Results indicate that the fracture exhibits differing effects regarding different trapping mechanisms. Generally speaking, highly-conductive fractures facilitate dissolution trapping while weakening residual trapping, and flow barriers can assist dissolution trapping for systems with a relatively low gravity number. The findings from the test cases for single fracture geometries are found applicable to a larger-scale domain with complex fracture networks. This indicates the scalability of the study for field-relevant applications.@en

Underground Hydrogen Storage (UHS) is a promising technology for large-scale energy storage. Geological formations, in which buoyant hydrocarbons have been retained for a long term, provide vast capacity for hydrogen storage in a safe manner. Different types of formations have been considered, such as salt caverns, saline aquifers, and depleted gas reservoirs. In this study we focus on saline aquifers. Although lessons were learnt from similar studies such as carbon capture and sequestration and underground gas storage, the unique thermodynamic and physical properties of hydrogen make UHS distinguished from the other subsurface storage projects. To this end, we developed a two-phase, three-component reservoir simulator, which incorporated essential physics based on the fully-coupled multi-physics framework of the DARSim simulator. Particularly, properties of fluid mixtures were computed using the thermodynamic model of GERG-2008. In the simulation, different types of cushion gases (CO2, CH4, and N2) were saturated at the top of the aquifer. Hydrogen was then injected into and produced from the aquifer periodically. Results showed that most of the injected hydrogen stayed at the top of the aquifer due to its light density, which led to a high extraction purity. The low solubility of hydrogen was favorable in UHS because dissolution trapping had a negligible impact. Our study confirmed the feasibility of large-scale underground hydrogen storage and showed the impact of different types of cushion gases on UHS.@en

The past decades have witnessed an increasing interest in numerical simulation for flow in fractured porous media. To date, most studies have focused on 2D or pseudo-3D computational models, where the impact of 3D complex structures on seepage has not been fully addressed. This work presents a method for modeling seepage in 3D heterogeneous porous media. The complex structures, typically the stochastic discrete fractures and inclusions, are able to be simulated. A mesh strategy is proposed to discretize the complex domain. In particular, a treatment on the intersected elements is developed to ensure a conforming mesh. Then, numerical discretization is provided, in which the flux interactions of fractures, inclusions and surrounding rock matrix are included. Numerical tests are performed to analyze the hydraulic characteristics of 3D fractured media. First, the developed framework is validated by comparing numerical solutions with the results of embedded discrete fracture model. Next, the effects of orientation, aperture and radius of fractures on fluid flow and equivalent permeability tensor are analyzed. The variations of pressure distribution are studied in heterogeneous and homogeneous media. Finally, the hydraulic properties of a medium with complex structures are investigated to show the difference of hydraulic feature between fractures and inclusions.

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CO2 injection into deep saline aquifers has shown to be a feasible option, as for their large storage capacity under safe operational conditions. Previous studies have revealed that CO2 can be trapped in the subsurface by several mechanisms. Despite the major advances in studying these trapping mechanisms, their dynamic interactions in different periods of a full-cycle process have not been well understood; i.e., they are studied independently at their so-called ‘separate time scales of importance’. These mechanisms, however, are dynamically interconnected and influence each other even outside of their main time scale of importance. Besides, previous studies on field-scale simulations often choose grid cells which are too coarse to capture flow dynamics especially in post-injection period. To this end, we develop a comprehensive framework to analyze the flow dynamics and the associated hydrodynamic trapping process, in which the CO2 injection, migration and post-migration period are all considered in a unified manner. Through illustrative models with sufficient grid resolution, we quantify the impact of different trapping mechanisms and uncertain reservoir properties through a full-cycle process. We demonstrate that the time scale associated with each trapping mechanism indeed varies, yet their dynamic interplay needs to be considered for accurate and reliable predictions. Results reveal that residual trapping is governed by the advective transport in the injection period, and its contribution to the overall trapped amount becomes more significant in systems with lower permeability. Dissolution trapping operates under varying driving forces at different stages. In the injection period, the dissolution process is controlled by advective transport, and later enhanced by the gravity-induced convection in the post-injection period. Such convective transport diminishes the contribution from residual trapping. Our study sheds light on the impact of the coupled reservoir and fluid time-dependent interactions in estimation of the securely trapped CO2 in saline aquifers. @en

Contamination caused by non-aqueous phase liquids (NAPLs) in aquifers and soil is an important challenge that requires effective remediation techniques. One potential approach is through the use of CO₂ foams to displace NAPLs from permeable media. CO₂ foams generated only by surfactants are not stable enough for the efficient removal of NAPLs contamination. This shortcoming may be alleviated via the use of nanoparticles (NPs)-surfactant mixtures as a stabilizing agent. This work focuses on the evaluation of the optimum concentration of fly ash nanoparticles for stabilizing CO₂ foam with the combined action of the surfactant. The performance of this foam is evaluated in remediating a contaminated 41 mm × 36 mm surrogate permeable medium in a microfluidic device. Mixtures of fly ash, a by-product of coal-burning power plants, and alpha-olefin sulfonate (AOS) and lauramidopropyl betaine (LAPB) surfactants are used to generate stable foams. The results show that a 1000 mg/L AOS-LAPB surfactant solution along with 1000 mg/L of fly ash NPs produces the best performance. Formation of deposits in the matrix is observed. These deposits, which are more prominent at higher NP concentrations, appear to adversely affect displacement, displacement efficiency and remediation of the medium. This study demonstrates that using fly ash nanoparticles and optimizing their concentration can effectively stabilize CO₂ foams and improve the displacement efficiency for aquifer and soil remediation.

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Shales will play an important role in the successful transition of energy from fossil-based resources to renewables in the coming decades. Aside from being a significant source of low-carbon intensity fuels, like natural gas, they also serve as geologic seals of subsurface formations that may be used to isolate nuclear waste, sequester CO₂, or store intermittent energy (e.g., solar hydrogen). Despite their importance, shales pose significant engineering and environmental challenges due to their nanoporous structure and extreme heterogeneity that spans at least ~10 orders of magnitude in spatial scale. Two challenges inhibit a system-level understanding: (1) the physics of fluid flow and phase behavior in shales are poorly understood due to the dominant molecular interactions between minerals and fluids under confinement, and (2) the apparent lack of scale separation that prevents a reliable (closed) description of the physics at any single scale of observation. In this review, we focus on the latter issue and discuss scale translation, which in its broadest sense is transforming data or simulations from one spatiotemporal scale to another. While effective scale translation is not exclusive to shales, but all geologic porous media, the need for it is especially acute in shales given their high degree of heterogeneity. Classical theories like homogenization, while indispensable, fail when scales are not separated. Other methods, like numerical upscaling, scale-translate in only one direction: small to large, but not the reverse, called downscaling. However, the confluence of advances in three areas are bringing challenging problems such as shales within reach: increased computational power and scalable algorithms; high-resolution imaging and multi-modal data acquisition; and machine learning to process massive amounts of data. While these advances equip geoscientists with a wide array of experimental and computational tools, no individual tool can probe the entire gamut of heterogeneity in shales. Their effective use, therefore, requires an ability to bridge between various data types obtained at different scales. The aim of this review is to present a coherent account of computational and experimental methods that may be used to achieve just that, i.e., to perform scale translation. We provide a broader definition of scale translation, one that transcends classical homogenization and upscaling methods, but is consistent with them and accommodates notions like downscaling and data translation. After a brief introduction to homogenization, we review hybrid methods, numerical upscaling and its recent extensions, multiscale computing, high-resolution imaging, and machine learning. We place particular emphasis on multiscale computing and propose an algorithmic framework to bridge between the pore (micro) and Darcy (macro) scales. Throughout the paper, we draw comparisons between the various methods and highlight their (often hidden) similarities, differences, benefits, and pitfalls. We finally conclude with two case studies on shales that exemplify some of the methods presented.

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Accurate prediction of flow behavior in shale matrix is critical for efficient development of shale gas reservoirs. In these systems, the majority of pores are in the nano-size range. As a result, continuum-based approaches may not be appropriate to simulate flow in such systems. Molecular dynamics (MD) simulations are capable of capturing the relevant microscale physics. Their relatively high computational expense, however, restricts MD simulations to rather small systems and domains. This limitation creates a gap between computational need of macroscale systems and capabilities of MD simulations. The lattice Boltzmann method (LBM) is a suitable candidate to bridge this gap. In this work, the multiple-relaxation-time (MRT)-LBM is used to study methane transport in nano-size pores. Adsorption effects near solid boundaries, as well as non-ideal behavior of fluids, are accounted for via incorporating appropriate force terms in LBM. Parameters associated with the force terms in the equation of state are studied in detail, and a workflow is proposed to determine optimal values of these parameters for gas flow in slit pores. Specifically, we establish these parameters such that the range of density values that the model is able to simulate is maximized. We demonstrate this workflow by simulating gas flow where velocity and density profiles from MD simulations are used as reference data. Results from LBM simulations are in good agreement with MD reference data for pores that are 4 nm in width or larger. Moreover, we propose a preconditioning scheme to improve the stability of LBM in dealing with complex geometries. The robustness of this scheme is demonstrated by simulating several roughness geometries. This work motivates the use of LBM in scale translation of the physics of mass transport in more complex permeable media.

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CO ₂ electroreduction offers a route to net-zero-emission production of C ₂H ₄—the most-produced organic compound. However, the formation of carbonate in this process causes loss of CO ₂ and a severe energy consumption/production penalty. Dividing the CO ₂-to-C ₂H ₄ process into two cascading steps—CO ₂ reduction to CO in a solid-oxide electrolysis cell (SOEC) and CO reduction to C ₂H ₄ in a membrane electrode assembly (MEA) electrolyser—would enable carbonate-free C ₂H ₄ electroproduction. However, this cascade approach requires CO-to-C ₂H ₄ with energy efficiency well beyond demonstrations to date. Here, we present a layered catalyst structure composed of a metallic Cu, N-tolyl-tetrahydro-bipyridine, and SSC ionomer that enables efficient CO-to-C ₂H ₄ in a MEA electrolyser. In the full SOEC-MEA cascade approach, we achieve CO ₂-to-C ₂H ₄ with no loss of CO ₂ to carbonate and a total energy requirement of ~138 GJ (ton C ₂H ₄) ⁻¹, representing a ~48% reduction in energy intensity compared with the direct route.

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