Underground hydrogen storage in depleted gas fields is a potential solution for large-scale, seasonal storage of hydrogen, in support of the decarbonization of energy systems and other industrial activities. Its viability depends on the performance of the storage operations, which is influenced by the interaction between reservoir geology and operational strategies. However, general guidelines for development planning that account for geological uncertainty are still lacking. In addition, existing site screening criteria remain limited in that they do not account for how operational decisions can alter the suitability of a reservoir geology for hydrogen storage. Here, we employ a numerical model of flow and transport to evaluate a set of operational strategies in varying geological scenarios for depleted methane gas reservoirs of the Bunter Sandstone, an important formation in the North Sea. We investigate the following strategies for their impact on performance and interaction with geological features that are common in the Bunter sandstone: depletion level, injected hydrogen mass, cushion gas, well perforation, idle period, production rates, and methane reinjection. We found that depletion level, injected mass, and well perforation interact strongly with geology and are critical for site selection. The methane reinjection strategy provides pressure support that increases hydrogen production, though at the cost of purity in the long-term. Furthermore, cushion gas strategies show significant optimization potential but limited interaction with geology, whereas the duration of the idle period and target rates have low optimization potential. Based on these findings, we propose a site selection and development planning framework for underground hydrogen storage in depleted gas fields. The site selection phase introduces a novel screening criterion, the gravity–purity number, which integrates geological and operational considerations. The development phase provides criteria and guidelines for planning operational strategies, and establishes a hierarchy based on their optimization potential.

Phase equilibrium calculations play an important role in a wide variety of applications in chemical and petroleum engineering. In this work, we focus on CO₂-hydrocarbon mixtures, with applications ranging from enhanced oil recovery processes to CO₂ storage. In compositional reservoir simulation, both robustness and efficiency are of utmost importance. The conventional approach for multiphase equilibrium consists of a sequence of phase stability and flash calculations. At each level of the stepwise process, stability testing is performed starting from several initial guesses; therefore, reducing the number of stability calls and using judiciously the information from stability to initialize a phase split are key points in developing an efficient stability-flash algorithm. Two new initialization strategies for multiphase flash calculations are proposed. The first one (improved stepwise initialization) follows the conventional procedure, but uses additional initial guesses. In the second one (improved multiple initialization), a three-phase split is initiated if at least three minima of the tangent plane distance (TPD) function are detected by stability analysis of feed composition. Both proposed methods are using all information from phase stability testing at each stage. Unlike in previous formulations, compositions at all minima of the TPD function, including trivial and positive TPDs are used to generate initial equilibrium constants. Highly robust routines are used, based on successive substitution iterations (SSI) in early iteration stages, followed by Newton iterations with modified Cholesky factorization and line search, in both stability and flash calculations. The proposed methods are tested and compared with the conventional procedure for several benchmark mixtures from the literature, containing hydrocarbon components and CO₂. Phase diagrams are constructed in the P-Z plane, focusing on the number of stationary points of the TPD functions found in each step of the multiphase stability-flash algorithm and on how they must be efficiently used in initialization. For all the test mixtures, in the proposed stability-flash strategy, the number of calls of the stability and flash routines and the number of iterations in flash calculations are significantly reduced as compared to previous approaches, recommending the new approach as a useful tool in compositional simulation.

In this work, we present a kinetic simulation model for gas hydrates in porous media using the Operator-Based Linearization (OBL) technique. The OBL approach introduces algebraic operators that represent the physical terms in the mass and energy balance equations. Operators are calculated only in supporting points comprising the discretized parameter space, and operator values and partial derivatives for linear system assembly are readily obtained through (multi-)linear interpolation. Taking advantage of this setup, the implementation of advanced thermodynamic models for hydrate formation and dissociation under kinetic assumptions is simplified. We test the assumptions for thermodynamic modelling by analysing the Gibbs energy surfaces of the fluid and hydrate phases and demonstrate that, in the limit, the thermodynamic equilibrium for both kinetic and equilibrium reaction models is equivalent. We compare the simulation results with the published experimental results for CH₄-hydrates and extend the assessment to a CO₂-hydrate formation experiment in a semi-batch, constant-pressure configuration. The model reproduces the main pressure–temperature transients and hydrate evolution for both CH₄- and CO₂-systems. We demonstrate applicability at core scale for hydrate formation and, at field scale, for gas production from CH₄-hydrates by thermal stimulation and depressurization. The interaction of thermal-compositional phenomena (phase changes, adiabatic expansion, kinetic rates, and reaction enthalpy) gives rise to highly nonlinear physics that an appropriate OBL discretization resolves. Overall, the patterns of hydrate formation and dissociation are highly sensitive to the kinetic-rate inputs; hence, the appropriate choice of the reaction model remains a key consideration from both physical and numerical perspectives.

Accurate characterization of subsurface heterogeneity is important for the safe and effective implementation of geological carbon storage (GCS) projects. This paper explores how machine learning methods can enhance data assimilation for GCS with a framework that integrates score-based diffusion models with machine learning-enhanced localization in channelized reservoirs during CO2 injection. We employ a machine learning-enhanced localization framework that uses large ensembles (Ns=5000) with permeabilities generated by the diffusion model and states computed by simple ML algorithms to improve covariance estimation for the Ensemble Smoother with Multiple Data Assimilation (ESMDA). We apply ML algorithms to a prior ensemble of channelized permeability fields, generated with the geostatistical model FLUVSIM. Our approach is applied on a CO2 injection scenario simulated using the Delft Advanced Research Terra Simulator (DARTS). Our ML-based localization maintains significantly more ensemble variance than when localization is not applied, while achieving comparable data-matching quality. This framework has practical implications for GCS projects, helping improve the reliability of uncertainty quantification for risk assessment.

Direct Use Geothermal Systems (DUGS) are rapidly and densely deployed to meet the growing demand for renewable energy with less carbon emissions globally. The simulation of DUGS can provide a reservoir-scale understanding of geothermal resource assessment, where the geothermal system's lifetime and the injection well Bottom Hole Pressure (BHP) are used as performance indicators. However, there are inherent errors from numerical simulations of any engineering problems, due to approximating continuous partial differential equations by their discretized approximation in time and space. In this work, we establish an optimal numerical setup with reduced errors across the homogeneous, stratified and heterogeneous models for the simulation of a geothermal system. Next, we develop a standardized method for calculating recoverable Heat In Place (HIP) and an analytical solution for evaluating the HIP recovery factor across various geological models using a single forward simulation. We present reference examples on the design of DUGS simulations using the open-source software Delft Advanced Research Terra Simulator (open-DARTS). The open-DARTS platform enables accurate and efficient sensitivity and uncertainty analysis. Using Distance-Based Generalized Sensitivity Analysis (DGSA), we identify reservoir depth and discharge rate as the most influential parameters for geothermal projects across all three types of geological models.

Physics-Informed Neural Networks (PINNs) gains attentions as a promising approach for applying deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, due to the challenging regions within the solutions of 'stiff' PDEs, e.g., shock front of CO₂ immiscible flooding, adaptive methods are essential to ensure the neural network accurately addresses these issues. In this work, we introduce a novel method for adaptively training PINNs, named Self-Adaptive PINNs (SA-PINNs). This approach employs fully trainable adaptation weights that are applied individually to each training point. Consequently, the neural network autonomously identifies challenging regions of the solution space and focuses its learning efforts on these areas. This method is hereby used to simulate a two-phase immiscible flooding in a low-permeability oil reservoir, with considering gas dissolution and the threshold pressure gradient of oil phase in low-permeability oil reservoirs, i.e., modified Buckley-Leverett (B-L) problem. The model is capable of generating a precise physical solution, accurately capturing both shock and rarefaction waves under the specified initial and boundary conditions, though the introduction of complicated physics increases the nonlinearity of the governing PDEs. The self-adaptive mechanism modifies the behavior of the deep neural network by simultaneously minimizing the losses and maximizing the weights. It, thus, can effectively capture the non-linear characteristics of the solution, thereby overcoming the existing limitations of PINNs. In these numerical experiments, the SA-PINNs demonstrated superior performance compared to other state-of-the-art PINN algorithms in terms of L2 error. Moreover, it was also achieved with a reduced number of training epochs. SA-PINNs can effectively model the dynamics of complex physical systems by optimizing network parameters to minimize the residuals of the PDEs.