Accurate simulation of multiphase flow is essential for predicting pressure buildup and CO₂ plume migration in geological carbon storage. The two-point flux approximation (TPFA) method is widely used in reservoir simulation due to its simplicity, but it is only consistent on K-orthogonal grids. Realistic subsurface models, however, often involve non-K-orthogonal grids caused by geological features such as faults and fractures, where TPFA may introduce significant errors. This study systematically quantifies the numerical error associated with using TPFA on non-K-orthogonal grids in the context of CO₂ storage in saline aquifers. Based on the formalism of the TPFA method, a numerical index is proposed in this work for the first time to quantify the degree of grid non-K-orthogonality. A series of numerical experiments are presented to compare the TPFA and multi-point flux approximation (MPFA) methods, with high-resolution reference solutions used as benchmarks. Results show that grid non-K-orthogonality can impact the accuracy of both TPFA and MPFA solutions with larger degree of grid non-K-orthogonality leading to larger solution errors in general. The magnitude of solution errors of the MPFA method is significantly smaller than that of TPFA in terms of both pressure solution and CO₂ saturation as it is much more robust against grid non-K-orthogonality effect. In particular, the TPFA method can produce substantial deviations in CO₂ saturation distributions when grid non-K-orthogonality is present, indicating the necessity of more advanced discretization methods such as MPFA for modeling the CO₂ plume migration behavior more accurately. These findings highlight the importance of selecting appropriate discretization methods for geologically complex reservoirs and the proposed grid non-K-orthogonality index can help evaluate the solution accuracy in a general simulation study. Our results offer practical guidance on the tradeoffs between computational efficiency and physical accuracy in carbon storage modeling.

Large-scale geological storages of hydrogen (H₂) and carbon dioxide (CO₂) in saline aquifers present feasible options for a sustainable energy future. We compared the plume migration of CO₂ and H₂ in aquifers using the FluidFlower benchmark, incorporating the state-of-the-art thermophysical and petrophysical properties. The H₂ plume, with its higher buoyancy and mobility compared to CO₂, remains predominantly in the gas phase due to its lower solubility, increasing the chances of escaping through fractures or migration to distant regions. This additionally leads to a higher pressurized reservoir, which, along with higher buoyancy, increases the chance of caprock penetration. Dissolution trapping of CO₂ into brine increases over time due to its fingering, while H₂ does not show fingering. Our findings show that while geological carbon storage (GCS) benefits significantly from all structural, dissolution, and residual trapping, underground hydrogen storage (UHS) relies mainly on structural trapping, making the integrity of sealing elements of the system a key factor in its performance.

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO) have demonstrated excellent generalization properties when mapping between spatial function spaces. However, they struggle in mapping the temporal dynamics of time-dependent PDEs, especially for time steps not explicitly seen during training. This limits their temporal accuracy as they do not leverage these dynamics in the training process. In addition, most NOs tend to be prohibitively costly to train, especially for higher-dimensional PDEs. In this paper, we propose the Temporal Neural Operator (TNO), an efficient neural operator specifically designed for spatio-temporal operator learning for time-dependent PDEs. TNO achieves this by introducing a temporal-branch to the DeepONet framework, leveraging the best architectural design choices from several other NOs, and a combination of training strategies including Markov assumption, teacher forcing, temporal bundling, and the flexibility to condition the output on the current state or past states. Through extensive benchmarking and an ablation study on a diverse set of example problems we demonstrate the TNO long range temporal extrapolation capabilities, robustness to error accumulation, resolution invariance, and flexibility to handle multiple input functions.

This work introduces a novel application of the Algebraic Dynamic Multilevel (ADM) method for simulating CO₂ storage in deep saline aquifers. By integrating a fully implicit coupling strategy, fully compositional thermodynamics, and adaptive mesh refinement, the ADM framework effectively models phenomena such as buoyancy-driven migration, convective dissolution, and phase partitioning under various subsurface conditions. The method starts with the construction of a hierarchy of multilevel grids and the generation of localized multiscale basis functions, which account for heterogeneities at each coarse level. During the simulation, the ADM method dynamically refines areas with significant overall CO₂ mass fraction gradients while coarsening smooth regions, thus optimizing computational resources without compromising the accuracy required to capture essential flow and transport characteristics. This dynamic grid adjustment is facilitated by algebraic prolongation and restriction operators, which map the fine-scale system onto a coarser grid suited to the evolving distribution of the CO₂ plume. This feature allows the ADM to navigate various coarsening thresholds efficiently, striking a trade-off between computational economy and detailed simulation accuracy. Even at relatively higher thresholds, key trapping mechanisms are captured with sufficient detail for quantification. These capabilities make the ADM framework well suited for long-term CO₂ sequestration in highly heterogeneous reservoirs, where large-scale models may otherwise become impractically expensive, offering a practical balance between the need for detailed simulations and manageable computational requirements. Overall, the ADM framework proves to be a robust tool for designing, monitoring, and analyzing large-scale CO₂ storage operations, supporting reliable and cost-effective solutions in carbon management.