Thermodynamic factors for diffusion connect the Fick and Maxwell-Stefan diffusion coefficients used to quantify mass transfer. Activity coefficient models or equations of state can be fitted to experimental or simulation data, from which thermodynamic factors can be obtained by differentiation. The accuracy of thermodynamic factors determined using indirect routes is dictated by the specific choice of an activity coefficient model or an equation of state. The Permuted Widom’s Test Particle Insertion (PWTPI) method developed by Balaji et al. enables direct determination of thermodynamic factors in binary and multicomponent systems. For highly dense systems, for example, typical liquids, it is well known that molecular test insertion methods fail. In this article, we use the Continuous Fractional Component Monte Carlo (CFCMC) method to directly calculate thermodynamic factors by adopting the PWTPI method. The CFCMC method uses fractional molecules whose interactions with their surrounding molecules are modulated by a coupling parameter. Even in highly dense systems, the CFCMC method efficiently handles molecule insertions and removals, overcoming the limitations of the PWTPI method. We show excellent agreement between the results of the PWTPI and CFCMC methods for the calculation of thermodynamic factors in binary systems of Lennard-Jones molecules and ternary systems of Weeks-Chandler-Andersen molecules. The CFCMC method applied to calculate the thermodynamic factors of realistic molecular systems consisting of binary mixtures of carbon dioxide and hydrogen agrees well with the NIST REFPROP database. Our study highlights the effectiveness of the CFCMC method in determining thermodynamic factors for diffusion, even in densely packed systems, using relatively small numbers of molecules.

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H₂-CO₂ mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H₂-CO₂ mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H₂ due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO₂, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO₂ content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO₂-H₂-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO₂ and H₂ in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO₂ in NaCl brine decreased in the ternary system compared to the binary CO₂-NaCl brine system, the solubility of H₂ in NaCl brine increased less in the ternary system compared to the binary H₂-NaCl brine system. The cooperative effect of H₂-CO₂ enhances the H₂ solubility while suppressing the CO₂ solubility. The water content in the gas phase was found to be intermediate between H₂-NaCl brine and CO₂-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO₂-H₂ mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H₂-CO₂ mixtures.

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The storage of renewable hydrogen in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. This raises concerns about the mechanical stability of salt caverns under such operational conditions. The use of appropriate constitutive models for salt mechanics is an important step in investigating this issue, therefore many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and parameter set represents the given rock, based on stress–strain data sets, remains an unsolved challenge. In this paper, for the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation data sets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is then achieved by framing the calibration process as an optimization problem, for which the global Particle Swarm Optimization algorithm is employed. To allow for dynamic data integration, a multi-step calibration strategy is developed for a situation where experiments are included one at a time, as they become available. Additionally, due to the existing mild heterogeneity in the experimental rock samples, our optimization strategy is made flexible to allow for this slight heterogeneity. The devised optimization strategy, based on the multi-physics comprehensive constitutive modeling framework, results in a single set of representative material properties of all the deformation data sets. As a rigorous mathematical analysis for the presented method and the lack of relevant experimental data sets, we consider a wide range of synthetic experimental data sets, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust. Moreover, the results become increasingly more accurate as more data sets become available.

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Underground hydrogen (H₂) storage in saline aquifers is a viable solution for large-scale H₂ storage. Due to its remarkably low viscosity and density, the flow of H₂ within saline aquifers exhibits strong instability, which needs to be thoroughly investigated to ensure safe operations at the storage site. For the first time, we develop a lattice Boltzmann model tailored for pore-scale simulations of the H₂-brine system under typical subsurface storage conditions. The model captures the significant contrast of fluid properties between H₂ and brine, and it offers the flexibility to adjust the contact angle to suit varying wetting conditions. We show that the snap-off is enhanced in a system with a high capillary number and a small contact angle. These conditions lead to a low recovery factor, which is unfavorable for H₂ production from the aquifer. Moreover, the relative permeability curves, computed from the simulation results, exhibit distinct behaviors for H₂ and brine. In the case of the wetting phase, the relative permeability can be quantified using the quadratic expression, whereas for the non-wetting phase, the relative permeability exhibits a nearly linear behavior, and saturation alone appears insufficient to characterize the relative permeability at large saturations of non-wetting phase. This implies that different formula for liquid and gas phases may be employed for continuum-scale simulations.

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Characterization of the microbial activity impacts on transport and storage of hydrogen is a crucial aspect of successful Underground Hydrogen Storage (UHS). Microbes can use hydrogen for their metabolism, which can then lead to formation of biofilms. Biofilms can potentially alter the wettability of the system and, consequently, impact the flow dynamics and trapping mechanisms in the reservoir. In this study, we investigate the impact of microbial activity on wettability of the hydrogen/brine/rock system, using the captive-bubble cell experimental approach. Apparent contact angles are measured for bubbles of pure hydrogen in contact with a solid surface inside a cell filled with living brine which contains sulphate reducing microbes. To investigate the impact of surface roughness, two different solid samples are used: a "rough" Bentheimer Sandstone sample and a "smooth" pure Quartz sample. It is found that, in systems where buoyancy and interfacial forces are the main acting forces, the impact of biofilm formation on the apparent contact angle highly depends on the surface roughness. For the "rough" Bentheimer sandstone, the apparent contact angle was unchanged by biofilm formation, while for the smooth pure Quartz sample the apparent contact angle decreased significantly, making the system more water-wet. This decrease in apparent contact angle is in contrast with an earlier study present in the literature where a significant increase in contact angle due to microbial activity was reported. The wettability of the biofilm is mainly determined by the consistency of the Extracellular Polymeric Substances (EPS) which depends on the growth conditions in the system. Therefore, to determine the impact of microbial activity on the wettability during UHS will require accurate replication of the reservoir conditions including surface roughness, chemical composition of the brine, the microbial community, as well as temperature, pressure and pH-value conditions.

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Large-scale storage technologies are crucial to balance consumption and intermittent production of renewable energy systems. One of these technologies can be developed by converting the excess energy into compressed air or hydrogen, i.e., compressed gas, and storing it in underground solution-mined salt caverns. Salt caverns are proven seals towards compressed air and hydrogen. However, several challenges, including fast injection/production cycles and operation of systems of caverns, are yet to be resolved to allow for a safe scale-up of energy storage in salt caverns. To address these challenges, it is important to identify key parameters that impact both the safety and efficiency of the operations. For this purpose, the present study conducts sensitivity analyses to show the importance of different parameters on the time-dependent mechanical behavior of salt caverns, individually and in a multi-cavern system. The impact of different deformation mechanisms (e.g. transient and reverse creep), model calibration, cavern shape, presence of interlayers and multi-cavern interactions are investigated in this study. The constitutive model adopted in this work and the mathematical formulation are presented in detail. Additionally, an open-source three-dimensional simulator, named “SafeInCave”, is developed for the numerical solution of the non-linear governing equations. The findings provide insights into improving the reliability of numerical simulations for the safe and efficient operation of salt caverns in energy storage applications.

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Hydrogen, regarded as a clean energy carrier, holds potential for subsurface porous media storage to balance energy supply and demand. Investigating the interactions between hydrogen and porous media, especially the potential residual trapping during cyclic injection and production, becomes imperative. Experimental studies were conducted to examine the influence of flow rate and cyclic injection/production on hydrogen storage and recovery efficiency. Findings reveal generally low hydrogen saturation in brine-saturated porous media during storage process, due to notable flow instability. However, higher injection rates contribute to increased hydrogen saturation. Moreover, observations indicate that cyclic hydrogen storage and drainage may lead to hysteresis in hydrogen storage process. That is, cyclic hydrogen storage and drainage may result in undesired residual trapping of hydrogen in porous media. This study underscores the need for a comprehensive investigation to validate these observations, shedding light on the complexities of hydrogen storage dynamics in subsurface porous media.@en

The modeling of fluid flow in heterogeneous, anisotropic and fractured porous media is relevant in many applications, including hydrocarbon and groundwater extraction, dispersion of contaminants, hydrogen or carbon dioxide (CO₂) storage. Thus, accurate and scalable simulation of fluid flow through these formations continues to be a great challenge. The presence of fractures that are explicitly modeled, ranging from flow barriers to highly conductive channels, significantly increases the complexity of the numerical simulation. The Embedded Discrete Fracture Model (EDFM) produces results that can be as accurate as those obtained using equidimensional Discrete Fracture Models (DFM) at a much lower computational cost for highly conductive fractures, but it is not adequate for impermeable barriers. In contrast, the pEDFM (projection-based Embedded Discrete Fracture Model) produces accurate results for both, channels and barriers by using additional matrix-fracture connectivities. In its current versions, it is restricted to cartesian and corner-point grid geometries and to the classical Two Point Flux Approximation (TPFA) scheme. In this work, for the first time, the pEDFM is extended to handle unstructured tetrahedral meshes (pEDFM-U). In addition, interface fluxes are approximated by using the Multipoint Flux Approximation method with a Diamond stencil (MPFA-D). This allows for simulation of highly heterogeneous and anisotropic geo-models. The developed method is robust and can deal with full permeability tensors on arbitrary tetrahedral meshes. The advective terms are discretized considering an implicit First Order Upwind (FOU) method. Our method is implemented within the DARSim (Delft Advanced Reservoir Simulation) open-source simulator framework. Through several test cases, the proposed method showed to be robust and capable to accurately capture the effects of both high and low permeability fractures for general tetrahedral meshes, under arbitrary heterogeneous and anisotropic permeability tensors for the rock matrix.

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CO₂ capture and storage is a viable solution in the effort to mitigate global climate change. Deep saline aquifers, in particular, have emerged as promising storage options, owing to their vast capacity and widespread distribution. However, the task of proficiently monitoring and simulating CO₂ behavior within these formations poses significant challenges. To address this, we introduce the physics-constraint neural network for CO₂ storage (CO₂PCNet), a model specifically designed for simulating and monitoring CO₂ storage in deep saline aquifers during injection and post-injection periods. Recognizing the significant challenges in accurately modeling the distribution and movement of CO₂ under varying permeability conditions, the CO₂PCNet integrates the principles of physics with the robustness of deep learning, serving as a powerful surrogate model. The architecture of CO₂PCNet starts with an encoder that adeptly processes spatial features from overall mole fraction (z_CO2) and pressure fields (P_l), capturing the complex dynamics of a CO₂ trajectory. By incorporating permeability information through a conditioning step, the network ensures a faithful representation of the influences on CO₂ behavior in subsurface conditions. A ConvLSTM module subsequently discerns temporal evolutions, reflecting the real-world progression of CO₂ plumes within the reservoir. Lastly, the decoder precisely reconstructs the predictive spatial profile of CO₂ distribution. CO₂PCNet, with its integration of convolutional layers, recurrent mechanisms, and physics-informed constraints, offers a refined approach to CO₂ storage simulation. This model offers the potential of utilizing advanced computational methods in advancing CCS practices.

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Considering the storage capacity and already existing infrastructures, underground porous reservoirs are highly suitable to store green energy, for example, in the form of green gases such as hydrogen and compressed air. Depending on the energy demand and supply, the energy-rich fluids are injected and produced, which induces cyclic change of state-of-the-stress in the reservoir and its surrounding. Detailed analyses of the geo-mechanical deformations under variable storage conditions i.e., storage frequency and fluid fluctuating pressures, are crucially important for safe and efficient operations. The present work presents an integrated analysis, based on experimental and constitutive modeling aspects, to investigate sandstones’ geomechanical response to cyclic loading relevant to underground energy storage (UES). To this end, sandstone rock samples were subjected to cyclic loading above and below the onset of dilatant cracking under different frequencies and loading amplitudes. Axial strains and Acoustic Emissions (AE) were measured in both regimes to quantify the total deformation (strain) of the rock and its AE characteristics. It is found that the inelastic strain and number of AE events is the highest in the first cycle and reduce subsequently cycle after cycle. Moreover, cyclic inelastic deformations are affected by the mean stress, amplitude, and frequency of the stress waveform. On the one hand, the higher the mean stress and the amplitude, the higher the total inelastic strains. On the other hand, the lower the frequency, the higher the total inelastic strain. From the modeling perspectives, five types of deformation mechanisms were identified based on the governing physics: elastic, viscoelastic, compaction-based cyclic inelastic, inelastic brittle creep, and dilatation-based inelastic deformation. To model elastic, viscoelastic, and brittle creep, the Nishihara model was used. A cyclic modified cam clay model (MCC) and hardening–softening model were applied to capture plastic deformation. The results show a very good fit of the constitutive model with the experimental results, which could help in studying the response of reservoirs to injection and production.

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Hydrogen is a promising energy carrier for a low-carbon future energy system, as it can be stored on a megaton scale (equivalent to TWh of energy) in subsurface reservoirs. However, safe and efficient underground hydrogen storage requires a thorough understanding of the geomechanics of the host rock under fluid pressure fluctuations. In this context, we summarize the current state of knowledge regarding geomechanics relevant to carbon dioxide and natural gas storage in salt caverns and depleted reservoirs. We further elaborate on how this knowledge can be applied to underground hydrogen storage. The primary focus lies on the mechanical response of rocks under cyclic hydrogen injection and production, fault reactivation, the impact of hydrogen on rock properties, and other associated risks and challenges. In addition, we discuss wellbore integrity from the perspective of underground hydrogen storage. The paper provides insights into the history of energy storage, laboratory scale experiments, and analytical and simulation studies at the field scale. We also emphasize the current knowledge gaps and the necessity to enhance our understanding of the geomechanical aspects of hydrogen storage. This involves developing predictive models coupled with laboratory scale and field-scale testing, along with benchmarking methodologies.

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Reservoir simulations for subsurface processes play an important role in successful deployment of geoscience applications such as geothermal energy extraction and geo-storage of fluids. These simulations provide time-lapse dynamics of the coupled poromechanical processes within the reservoir and its over-, under-, and side-burden environments. For more reliable operations, it is crucial to connect these reservoir simulation results with the seismic surveys (i.e., observation data). However, despite being crucial, such integration is challenging due to the fact that the reservoir dynamics alters the seismic parameters. In this work, a coupled reservoir simulation and time-lapse seismic methodology is developed for multiphase flow operations in subsurface reservoirs. To this end, a poromechanical simulator is designed for multiphase flow and connected to a forward seismic modeller. This simulator is then used to assess a novel methodology of seismic monitoring by isolating the reservoir signal from the entire reflection response. This methodology is shown to be able to track the development of the fluid front over time, even in the presence of a highly reflective overburden with strong time-lapse variations. These results suggest that the proposed methodology can contribute to a better understanding of fluid flow in the subsurface. Ultimately, this will lead to improved monitoring of reservoirs for underground energy storage or production.

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This poster outlines a hierarchical, multiscale modelling approach that is adapted from proven hydrocarbon reservoir characterization workflows to determine which 3D sedimentological and stratigraphic heterogeneity types at which temporal and spatial scales and in which configurations are most important for successful long-term CO2 storage. The approach is particularly in saline aquifers that are data-poor but have the potential to store large CO2 volumes. It uses the Representative Element Volume (REV) concept and associated upscaling methodology to characterise sedimentological heterogeneity types, and it leverages novel modelling tools that facilitate rapid model construction and prototyping, geometrically accurate representation of key geological heterogeneities in models, and computationally efficient simulation of all CO2 trapping mechanisms over relevant spatial and temporal scales.@en

Underground Hydrogen Storage (UHS) is an emerging large-scale energy storage technology. Researchers are investigating its feasibility and performance, including its injectivity, productivity, and storage capacity through numerical simulations. However, several ad-hoc relative permeability and capillary pressure functions have been used in the literature, with no direct link to the underlying physics of the hydrogen storage and production process. Recent relative permeability measurements for the hydrogen-brine system show very low hydrogen relative permeability and strong liquid phase hysteresis, very different to what has been observed for other fluid systems for the same rock type. This raises the concern as to what extend the existing studies in the literature are able to reliably quantify the feasibility of the potential storage projects. In this study, we investigate how experimentally measured hydrogen-brine relative permeability hysteresis affects the performance of UHS projects through numerical reservoir simulations. Relative permeability data measured during a hydrogen-water core-flooding experiment within ADMIRE project is used to design a relative permeability hysteresis model. Next, numerical simulation for a UHS project in a generic braided-fluvial water-gas reservoir is performed using this hysteresis model. A performance assessment is carried out for several UHS scenarios with different drainage relative permeability curves, hysteresis model coefficients, and injection/production rates. Our results show that both gas and liquid relative permeability hysteresis play an important role in UHS irrespective of injection/production rate. Ignoring gas hysteresis may cause up to 338% of uncertainty on cumulative hydrogen production, as it has negative effects on injectivity and productivity due to the resulting limited variation range of gas saturation and pressure during cyclic operations. In contrast, hysteresis in the liquid phase relative permeability resolves this issue to some extent by improving the displacement of the liquid phase. Finally, implementing relative permeability curves from other fluid systems during UHS performance assessment will cause uncertainty in terms of gas saturation and up to 141% underestimation on cumulative hydrogen production. These observations illustrate the importance of using relative permeability curves characteristic of hydrogen-brine system for assessing the UHS performances.

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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

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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Data for several key thermodynamic and transport properties needed for technologies using hydrogen (H₂), such as underground H₂ storage and H₂O electrolysis are scarce or completely missing. Force field-based Molecular Dynamics (MD) and Continuous Fractional Component Monte Carlo (CFCMC) simulations are carried out in this work to cover this gap. Extensive new data sets are provided for (a) interfacial tensions of H₂ gas in contact with aqueous NaCl solutions for temperatures of (298 to 523) K, pressures of (1 to 600) bar, and molalities of (0 to 6) mol NaCl/kg H₂O, (b) self-diffusivities of infinitely diluted H₂ in aqueous NaCl solutions for temperatures of (298 to 723) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H₂O, and (c) solubilities of H₂ in aqueous NaCl solutions for temperatures of (298 to 363) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H₂O. The force fields used are the TIP4P/2005 for H₂O, the Madrid-2019 and the Madrid-Transport for NaCl, and the Vrabec and Marx for H₂. Excellent agreement between the simulation results and available experimental data is found with average deviations lower than 10%.

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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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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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