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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., Reservoir Engineering, Engineering Thermodynamics

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., Reservoir Engineering, Mechanical Engineering, Applied Sciences

19 januari 2023, Item does not contain fulltext

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., Reservoir Engineering, Applied Geophysics and Petrophysics, Applied Mechanics

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 (Rs) and gas saturation (Sg) – 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 Rs and Sg. 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., Aerodynamics, Reservoir Engineering

Gigatonne scale geological storage of carbon dioxide and energy (such as hydrogen) will be central aspects of a sustainable energy future, both for mitigating CO2 emissions and providing seasonal-based green energy provisions. In this Review, we evaluate the feasibility and challenges of expanding subsurface carbon dioxide storage into a global-scale business, and explore how this experience can be exploited to accelerate the development of underground hydrogen storage. Carbon storage is technically and commercially successful at the megatonne scale, with current projects mitigating approximately 30 Mt of CO2 per year. However, limiting anthropogenic warming to 1.5°C could require gigatonnes of storage per year by 2050, and a scaleup from 2025 approaching rates of deployment that would be historic for energy technology. Scale-up is not limited by geology or engineering. Advances in understanding storage complex geology, subsurface fluid dynamics, and seismic risk underpin new engineering strategies including the development of multi-site, basin scale, storage resource management. Instead economic and societal contraints pose barriers to project development. Underground hydrogen storage, still in development, will face similar issues. Overcoming these barriers with strengthened financial incentives, and programs to address concerns inhibiting public acceptance, will enable the storage of CO2 at climate relevant scales., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Reservoir Engineering

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., Applied Geology, Reservoir Engineering

Successful transition to renewable energy supply depends on the development of cost-effective large-scale energy storage technologies. Renewable energy can be converted to (or produced directly in the form of) green gases, such as hydrogen. Subsurface formations offer feasible solutions to store large-scale compressed hydrogen. These reservoirs act as seasonal storage or buffer to guarantee a reliable supply of green energy in the network. The vital ingredients that need to be considered for safe and efficient underground hydrogen storage include reliable estimations of the in-situ state of the stress, especially to avoid failure, induced seismicity and surface subsidence (or uplift). Geological formations are often highly heterogeneous over their large (km) length scales, and entail complex nonlinear rock deformation physics, especially under cyclic loading. We develop a multiscale simulation strategy to address these challenges and allow for efficient, yet accurate, simulation of nonlinear elastoplastic deformation of rocks under cyclic loading. A coarse-scale system is constructed for the given fine-scale detailed nonlinear deformation model. The multiscale method is developed algebraically to allow for convenient uncertainty quantifications and sensitivity analyses., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Reservoir Engineering

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., Applied Geophysics and Petrophysics, Reservoir Engineering

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., Applied Geology, Reservoir Engineering, Numerical Analysis

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., Numerical Analysis, Reservoir Engineering

In fractured geological formations, as a result of the in-situ stress changes, fractures can propagate or slide. This phenomenon can be efficiently modeled by the extended finite element method (XFEM) when there are only a few fractures present. However, geological reservoirs contain many fractures which can also cross and are densely populated. Therefore, the classical XFEM is too expensive to be applied for the simulation of propagating fractures in geological formations. To reduce the costs, typically, homogenization or upscaling is used. However, they result in inaccurate solutions, since no separation of scales exists in this process. To resolve this challenge, in this work, a multiscale XFEM (MS-XFEM) for propagating fractures is developed and presented. In each time step, given the current geometries of the fractures, local XFEM-based basis functions are constructed or adaptively updated. The adaptive update takes place in certain regions where fracture geometries are changed due to propagation. Using these basis functions, a very efficient FEM-based coarse-scale system is developed since it has no extra degrees of freedom (DOFs). Once the coarse-scale system is solved, its solution is prolonged to the fine-scale original resolution using the basis functions. This approximate fine-scale solution is then used to estimate the group of growing fractures tips and their growing angles. This allows for exploiting the locality of the propagation process fully while solving a global system. To control the error, an iterative procedure is also developed. Proof-of-concept test cases are presented to study the developed MS-XFEM algorithm. It is shown that MS-XFEM results are capable of predicting the propagating paths for complicated fracture patterns. As such, MS-XFEM casts a promising method for field-scale applications., Applied Mechanics, Reservoir Engineering, Materials- Mechanics- Management & Design

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%., Geoscience and Engineering, Engineering Thermodynamics, Team Poulumi Dey

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 wh, Numerical Analysis, Reservoir Engineering

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., Numerical Analysis, Geoscience and Engineering, Civil Engineering & Geosciences, Reservoir Engineering

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 permeabilit, Reservoir Engineering

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 a, Applied Geophysics and Petrophysics, Reservoir Engineering

Unconventional reservoir resources are important to supplement energy consumption and maintain the balance of supply and demand in the oil and gas market. However, due to the complex geological conditions, it is a significant challenge to develop unconventional reservoirs efficiently and economically. At present, unconventional reservoirs are extensively studied, covering a wide range of areas, with special attention to the multiscale characterization of pore structures and fracture networks, description of complex fluid transport mechanisms, mathematical modeling of flow properties, and coupled analysis with multiphysics fields. This work briefly describes the multiscale and multiphysics influences on fluids in unconventional reservoirs, and the modeling and simulation work conducted to analyze them, with the aim to provide some theoretical basis for enhanced recovery from these geo-energy resources. The present article also aims to enhance the community’s knowledge of other potential utilizations associated with some unconventional reservoirs, specially related to environmentally-driven projects, including permanent greenhouse gas storage and cyclic underground energy storage., Petroleum Engineering

Simulation of fracture contact mechanics in deformable fractured media is of paramount important in computational mechanics. Previous studies have revealed that compressive loading may produce mode II fractures, which is quite different from mode I fractures induced by tensile loading. Furthermore, fractures can cross each other. This will increase the complexity of their network deformation under different loading types significantly. In this work, a stabilized mixed-finite element (FE) scheme with Lagrange multipliers is proposed in the framework of variational formulation, which is able to simulate frictional contact, shear failure (mode II) and opening (mode I) of multiple crossing fractures. A novel treatment is devised to guarantee physical solutions at the intersection of crossing fractures. A preconditioner is introduced to re-scale the saddle-point algebraic system and to preserve the numerical robustness. Then, a solution strategy is designed to calculate the unknowns, displacement and Lagrange multipliers, in one algebraic system. Later, numerical tests are conducted to study mechanical behaviors of fractured media. Benchmark study is performed to verify the presented mixed-FE scheme. A deformable medium with crossing fractures is simulated under mixed-mode loading types. The characteristics of fracture contact, surface sliding, opening and variation of stress intensity factor are analyzed. Simulation results show that the curve of slippage induced by compression, as well as the opening induced by internal fluid pressure, along the fracture length holds a parabolic shape. The diagonal contact point, at the intersecting position of the crossing fractures, is studied in detail, specially under different stress states. Finally, the impact of intersecting fractures on frictional contact mechanics is investigated for different loading conditions., Numerical Analysis, Delft Institute of Applied Mathematics, Petroleum Engineering

A smoothed embedded finite-volume modeling (sEFVM) method is presented for faulted and fractured heterogeneous poroelastic media. The method casts a fully coupled strategy to treat the coupling between fault slip mechanics, deformation mechanics, and fluid flow equations. This ensures the stability and consistency of the simulation results, especially, as the fault slip is implicitly found through an iterative prediction-correction procedure. The computational grid is generated independently for embedded faults and rock matrix. The efficiency is further enhanced by extending the finite-volume discrete space by introducing only one degree of freedom per fault element. The embedded approach can lead to an oscillatory stress field at the fault, which damages the robustness of the implicit slip detection strategy. To resolve this challenge, a smoothed embedded strategy is devised, in which the stress and slip profiles are post processed within the iterative loops by fitting the best curve based on a least-square error criterion. The sEFVM provides locally conservative mass flux and stress fields, on staggered grid. Its performance is further investigated for several proof-of-the-concept test cases, including a multiple fault system in a heterogeneous domain. Results indicate that the method develops a promising approach for field-scale relevant simulation of induced seismicity., Petroleum Engineering, Civil Engineering and Geosciences

We present the projection-based embedded discrete fracture model (pEDFM) for hexahedral corner-point grid (CPG) geometries, for the simulation of hydrothermal processes in fractured porous media. Unlike the previously-developed pEDFM for structured box grids, our new development allows for the modeling of complex geometries defined with hexahedral CPG cells. It also advances the pEDFM method to include coupled flow and heat transfer systems. Mass and energy conservation equations are simulated in a fully-coupled manner using a fully-implicit (FIM) integration scheme. This allows for stable simulations, specially when large time steps are taken. Independent corner-point grids are imposed on the rock matrix and all fractures, with conductivities ranging from highly permeable to flow barriers. The connectivities between the non-neighboring grid cells are described such that a consistent discrete representation of the embedded fractures occurs within the corner-point grid geometry, specially as the quadrilateral interfaces are allowed to be fully flexible. Various numerical tests including geologically-relevant and real-field models, which are established in the literature, are conducted to demonstrate the applicability of the developed method. It is shown that pEDFM can accurately capture the physical influence of both highly conductive fractures and flow barriers on the flow and heat transfer fields in complex reservoir geometries. This development is promising for flow simulations of real-field geo-models, increasing the discretization flexibility and enhancing the computational performance for capturing explicit fractures accurately., Numerical Analysis, Petroleum Engineering

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., Numerical Analysis, Petroleum Engineering

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 a, Numerical Analysis, Petroleum Engineering

Characterizing the wettability of hydrogen (H2)–methane (CH4) mixtures in subsurface reservoirs is the first step towards understanding containment and transport properties for underground hydrogen storage (UHS). In this study, we investigate the static contact angles of H2–CH4 mixtures, in contact with brine and Bentheimer sandstone rock using a captive-bubble cell device at different pressures, temperatures and brine salinity values. It is found that, under the studied conditions, H2 and CH4 show comparable wettability behaviour with contact angles ranging between [25°–45°]; and consequently their mixtures behave similar to the pure gas systems, independent of composition, pressure, temperature and salinity. For the system at rest, the acting buoyancy and surface forces allow for theoretical sensitivity analysis for the captive-bubble cell approach to characterize the wettability. Moreover, it is theoretically validated that under similar Bond numbers and similar bubble sizes, the contact angles of H2 and CH4 bubbles and their mixtures are indeed comparable. Consequently, in large-scale subsurface storage systems where buoyancy and capillary are the main acting forces, H2, CH4 and their mixtures will have similar wettability characteristics., Numerical Analysis, Petroleum Engineering

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., Numerical Analysis, Delft Institute of Applied Mathematics, Petroleum Engineering

An increasing number of geo-energy applications require the quantitative prediction of hydromechanical response in subsurface. Integration of mass, momentum, and energy conservation laws becomes essential for performance and risk analysis of enhanced geothermal systems, stability assessment of CO2 sequestration and hydrogen storage, resolving the issue of induced seismicity. The latter problem is of particular interest because it exposes safety risks to people and surface infrastructure. Implicit coupling of conservation laws is computationally demanding and the solution procedure often uses different numerical methods for different laws that complicates simulation. Recently developed Finite Volume (FV) schemes for poromechanics present a unified approach for the modeling of conservation laws in geo-energy applications. Contact mechanics at faults requires special attention due to the inequality constraints it imposes and nonlinear friction laws that strongly affect the occurrence of seismicity. We develop a cell-centered FV scheme for the purpose of integrated simulation in Delft Advanced Research Terra Simulator (DARTS) platform. The scheme proposes a unified numerical framework capable to resolve conservation laws in a fully implicit manner using a single collocated grid. Coupled multi-point flux and multi-point stress approximations provide mass, momentum, and heat fluxes at the faces of the computational grid. We use a conformal discrete fracture model to incorporate faults, where the multi-point approximations of fluxes respect the discontinuity in displacements. The block-partitioned preconditioner that takes the advantage of linear structure of the coupled problem is developed to facilitate the performance of the simulation. The proposed numerical scheme are validated against analytical and numerical solutions in a number of test cases. The convergence and stability of the schemes are investigated. It is found that the developed sc, Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Reservoir Engineering, Civil Engineering & Geosciences

Altering the state of the stress of the subsurface reservoirs can lead fractures to slip and extend their lengths (i.e., to propagate). This process can even be engineered, in many applications, e.g., enhanced geothermal systems. As such, accurate and efficient simulation of the mechanical deformation of the subsurface geological reservoirs, allowing for fracture propagation, is at the core of many geoscientific operational designs. Subsurface reservoirs entail many fractures at multiple scales. Implementation of 3D complex grids on these complex fractured systems, for mechanical deformation analyses, is extremely challenging. An alternative approach can be developed by using extended finite element methods (XFEM). XFEM allows for capturing the fractures effects on a conveniently-generated structured matrix mesh. The cracks are introduced by extra degrees of freedom (DOFs) on the nodes of the matrix rock mesh. For geoscientific applications, however, XFEM results in too many DOFs which are beyond the scope of simulators. Additionally, for propagating fractures, these DOFs need to be updated in response to the dynamic extension of the fractures in the domain. The propagation process not only adds to the sensitivity of the outputs to the accuracy of the estimated stress field, but also increases the size of the linear systems. In addition to these, matrix rocks are often highly heterogeneous, at high resolutions. In this work, we present a novel multiscale procedure for propagating fractures in heterogeneous geological reservoirs. For the first time in the community, we present the highly fractured systems at coarser resolutions via XFEM-based basis functions, which also account for the propagating effects. Fractures are allowed to extend their scale and the enriched basis functions are locally updated. Using these bases, the coarse scale system is obtained in which no extra DOFs due to fractures exist. This significantly reduces the computational complexity. As a, Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Electrical Engineering, Mathematics and Computer Science, Reservoir Engineering, Materials- Mechanics- Management & Design

Underground energy storage (UES) in porous and cavity reservoirs can be used to balance the mismatch between the production and demand of renewable energy. Understanding the geomechanical behaviour of these reservoirs under different storage conditions, i.e., storage frequency and fluid pressure, is key in defining their capacity and effective lifetime. This work presents an analysis performed on sandstones to unravel their geomechanical response under cyclic loading. It includes, importantly, both experimental and numerical investigations under deviatoric stress conditions below the rock dilatant cracking threshold. From the experimental point of view, axial strains and acoustic emissions indicated that inelastic strains accumulated cycle after cycle, following a decreasing rate per cycle. Four types of deformations were interpreted: elastic, viscoelastic, plastic, and cyclic-plastic. Based on these experimental results and observations, the Modified Cam-clay model was extended to account for cyclic plastic deformations and the Kelvin-Voigt model was used to model visco-elasticity. This approach can be used to study cyclic sandstone deformation’s implications on subsidence, fault reactivation, and cap rock flexure, among other physical phenomena impacting a reservoir’s storage capacity., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Applied Geophysics and Petrophysics, Reservoir Engineering

Subsurface geological formations can be utilized to safely store large-scale (TWh) renewable energy in the form of green gases such as hydrogen. Successful implementation of this technology involves estimating feasible storage sites, including rigorous mechanical safety analyses. Geological formations are often highly heterogeneous and entail complex nonlinear inelastic rock deformation physics when utilized for cyclic energy storage. In this work, we present a novel scalable computational framework to analyse the impact of nonlinear deformation of porous reservoirs under cyclic loading. The proposed methodology includes three different time-dependent nonlinear constitutive models to appropriately describe the behavior of sandstone, shale rock and salt rock. These constitutive models are studied and benchmarked against both numerical and experimental results in the literature. An implicit time-integration scheme is developed to preserve the stability of the simulation. In order to ensure its scalability, the numerical strategy adopts a multiscale finite element formulation, in which coarse scale systems with locally-computed basis functions are constructed and solved. Further, the effect of heterogeneity on the results and estimation of deformation is analyzed. Lastly, the Bergermeer test case—an active Dutch natural gas storage field—is studied to investigate the influence of inelastic deformation on the uplift caused by cyclic injection and production of gas. The present study shows acceptable subsidence predictions in this field-scale test, once the properties of the finite element representative elementary volumes are tuned with the experimental data., Reservoir Engineering

We present a scalable collocated Finite Volume Method (FVM) to simulate induced seismicity as a result of pore pressure changes. A discrete system is obtained based on a fully-implicit fully-coupled description of flow, elastic deformation, and contact mechanics at fault surfaces on a flexible unstructured mesh. The cell-centered collocated scheme leads to a convenient integration of the different physical equations, as the unknowns share the same discrete locations on the mesh. Additionally, a generic multi-point flux approximation is formulated to treat heterogeneity, anisotropy, and cross-derivative terms for both flow and mechanics equations. The resulting system, though flexible and accurate, can lead to excessive computational costs for field-relevant applications. To resolve this limitation, a scalable processing algorithm is developed and presented. Several proof-of-concept numerical tests, including benchmark studies with analytical solutions, are investigated. It is found that the presented method is indeed accurate and efficient; and provides a promising framework for accurate and efficient simulation of induced seismicity in various geoscientific applications., Reservoir Engineering, Civil Engineering & Geosciences

This paper presents an assessment of the life-cycle exergetic efficiency and CO2 footprint of the underground biomethanation process. The subsurface formation, hosting microorganisms required for the reaction, is utilized to convert CO2 and green (produced from renewable energy) hydrogen to the so-called "green"or synthetic methane. The net exergy gain and CO2 intensity of the biomethanation process are compared to the alternative options of (1) green H2 storage (no energy upgrading process to CH4) and (2) fossil-based CH4 with carbon capture and storage (CCS), i.e., blue CH4. It is found that with the current state of the technology and within the assumptions of this study, the exergy return on the exergy invested for underground biomethanation does not outperform the direct storage and utilization of green H2. The maximum exergetic efficiency of the biomethanation process is calculated to be 15-33% for electricity and 36-47% for heating, while the overall exergetic efficiency of the direct use of H2 for electricity is estimated to be between 20 and 61%. Moreover, the energy produced from the underground biomethanation process has the largest CO2 intensity among the studied options. Depending on the technology used in the CCS and hydrogen production stages, the CO2 intensity of the electricity generated from synthetic CH4 can be as large as 142 g CO2/MJe, which is at least 56-73% larger than those of the two other studied cases., Reservoir Engineering

Geological porous reservoirs provide the volume capacity needed for large scale underground hydrogen storage (UHS). To effectively exploit these reservoirs for UHS, it is crucial to characterize the hydrogen transport properties inside porous rocks. In this work, for the first time in the community, we have performed H 2/water multiphase flow experiments at core scale under medical X-ray CT scanner. This has allowed us to directly image the complex transport properties of H 2 when it is injected or retracted from the porous rock. The important effective functions of capillary pressure and relative permeability are also measured, for both drainage and imbibition. The capillary pressure measurements are combined with MICP data to derive a receding contact angle for the H 2/water/sandstone rock system. The rock core sample is a heterogeneous Berea sandstone (17 cm long and 3.8 cm diameter). Our investigation reveals the interplay between gravitational, capillary, and viscous forces. More specifically, it illustrates complex displacement patterns in the rock, including gravity segregation, enhancement of spreading of H 2 due to capillary barriers, and the formation of fingers/channel during imbibition which lead to significant trapping of hydrogen. These findings shed new light on our fundamental understanding of the transport characteristics of H 2/water relevant for UHS., Reservoir Engineering

A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly, Petroleum Engineering

Subsurface porous formations provide large capacities for underground hydrogen storage (UHS). Successful utilization of these porous reservoirs for UHS depends on accurate quantification of the hydrogen transport characteristics at continuum (macro) scale, specially in contact with other reservoir fluids. Relative-permeability and capillary-pressure curves are among the macro-scale transport characteristics which play crucial roles in quantification of the storage capacity and efficiency. For a given rock sample, these functions can be determined if pore-scale (micro-scale) surface properties, specially contact angles, are known. For hydrogen/brine/rock system, these properties are yet to a large extent unknown. In this study, we characterize the contact angles of hydrogen in contact with brine and Bentheimer and Berea sandstones at various pressure, temperature, and brine salinity using captive-bubble method. The experiments are conducted close to the in-situ conditions, which resulted in water-wet intrinsic contact angles, about 25 to 45 degrees. Moreover, no meaningful correlation was found with changing tested parameters. We monitor the bubbles over time and report the average contact angles with their minimum and maximum variations. Given rock pore structures, using the contact angles reported in this study, one can define relative-permeability and capillary-pressure functions for reservoir-scale simulations and storage optimization., Petroleum Engineering

Subsurface geological formations provide giant capacities for large-scale (TWh) storage of renewable energy, once this energy (e.g. from solar and wind power plants) is converted to green gases, e.g. hydrogen. The critical aspects of developing this technology to full-scale will involve estimation of storage capacity, safety, and efficiency of a subsurface formation. Geological formations are often highly heterogeneous and, when utilized for cyclic energy storage, entail complex nonlinear rock deformation physics. In this work, we present a novel computational framework to study rock deformation under cyclic loading, in presence of nonlinear time-dependent creep physics. Both classical and relaxation creep methodologies are employed to analyze the variation of the total strain in the specimen over time. Implicit time-integration scheme is employed to preserve numerical stability, due to the nonlinear process. Once the computational framework is consistently defined using finite element method on the fine scale, a multiscale strategy is developed to represent the nonlinear deformation not only at fine but also coarser scales. This is achieved by developing locally computed finite element basis functions at coarse scale. The developed multiscale method also allows for iterative error reduction to any desired level, after being paired with a fine-scale smoother. Numerical test cases are studied to investigate various aspects of the developed computational workflow, from benchmarking with experiments to analysing the impact of nonlinear deformation for a field-scale relevant environment. Results indicate the applicability of the developed multiscale method in order to employ nonlinear physics in their laboratory-based scale of relevance (i.e., fine scale), yet perform field-relevant simulations. The developed simulator is made publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/mechanics., Petroleum Engineering

Underground hydrogen storage (UHS) in initially brine-saturated deep porous rocks is a promising large-scale energy storage technology, due to hydrogen's high specific energy capacity and the high volumetric capacity of aquifers. Appropriate selection of a feasible and safe storage site vitally depends on understanding hydrogen transport characteristics in the subsurface. Unfortunately there exist no robust experimental analyses in the literature to properly characterise this complex process. As such, in this work, we present a systematic pore-scale modelling study to quantify the crucial reservoir-scale functions of relative permeability and capillary pressure and their dependencies on fluid and reservoir rock conditions. To conduct a conclusive study, in the absence of sufficient experimental data, a rigorous sensitivity analysis has been performed to quantify the impacts of uncertain fluid and rock properties on these upscaled functions. The parameters are varied around a base-case, which is obtained through matching to the existing experimental study. Moreover, cyclic hysteretic multiphase flow is also studied, which is a relevant aspect for cyclic hydrogen-brine energy storage projects. The present study applies pore-scale analysis to predict the flow of hydrogen in storage formations, and to quantify the sensitivity to the micro-scale characteristics of contact angle (i.e., wettability) and porous rock structure., Petroleum Engineering

Deformable fractured porous media appear in many geoscience applications. While the extended finite element method (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of deformation, its application in geoscientific applications is not straightforward. This is mainly due to the fact that subsurface formations are heterogeneous and span large length scales with many fractures at different scales. To resolve this limitation, in this work, we propose a novel multiscale formulation for XFEM, based on locally computed enriched basis functions. The local multiscale basis functions capture heterogeneity of th e porous rock properties, and discontinuities introduced by the fractures. In order to preserve accuracy of these basis functions, reduced-dimensional boundary conditions are set as localization condition. Using these multiscale bases, a multiscale coarse-scale system is then governed algebraically and solved. The coarse scale system entails no enrichment due to the fractures. Such formulation allows for significant computational cost reduction, at the same time, it preserves the accuracy of the discrete displacement vector space. The coarse-scale solution is finally interpolated back to the fine scale system, using the same multiscale basis functions. The proposed multiscale XFEM (MS-XFEM) is also integrated within a two-stage algebraic iterative solver, through which error reduction to any desired level can be achieved. Several proof-of-concept numerical tests are presented to assess the performance of the developed method. It is shown that the MS-XFEM is accurate, when compared with the fine-scale reference XFEM solutions. At the same time, it is significantly more efficient than the XFEM on fine-scale resolution, as it significantly reduces the size of the linear systems. As such, it develops a promising scalable XFEM method for large-scale heavily fractured porous media., Applied Mechanics, Petroleum Engineering, Materials- Mechanics- Management & Design