The SPE11 comparative solution project presents a benchmark for geological carbon storage in an aquifer, as the development of sufficiently accurate CO₂ sequestration models is critical for predicting the distribution of CO₂ during and after injection. In this paper we present a convergence analysis of the SPE11 benchmark simulation using the Delft Advanced Research Terra Simulator (open-DARTS). Open-DARTS, an open-source simulation framework designed for forward and inverse modeling, as well as uncertainty quantification, employs a unified thermal-compositional formulation and operator-based linearization. In our convergence analysis the SPE11b (2D - reservoir conditions) starts to converge at a grid resolution of 1340 × 240, after which added resolution provides diminishing returns. In addition the three-dimensional SPE11c benchmark is simulated with 8M grid blocks. However, 2D results from SPE11b suggest that a greater resolution is required for a truly converged solution. Furthermore, we extend the SPE11b benchmark to include H₂S as a trace impurity in the injection stream.

The 11th Society of Petroleum Engineers Comparative Solution Project (shortened SPE11 herein) benchmarked simulation tools for geological carbon dioxide (CO2) storage. A total of 45 groups from leading research institutions and industry across the globe signed up to participate, with 18 ultimately contributing valid results that were included in the comparative study reported here. This paper summarizes the SPE11 results. A comprehensive introduction and qualitative discussion of the submitted data are provided, together with an overview of online resources for accessing the full depth of data. A global metric for analyzing the relative distance between submissions is proposed and used to conduct a quantitative analysis of the submissions. This analysis attempts to statistically resolve the key aspects influencing the variability between submissions. The study shows that the major qualitative variation between the submitted results is related to thermal effects, dissolution-driven convective mixing, and resolution of facies discontinuities. Moreover, a strong dependence on grid resolution is observed across all three versions of the SPE11. However, our quantitative analysis suggests that the observed variations are predominantly influenced by factors not documented in the technical responses provided by the participants. We therefore identify that unreported variations due to human choices within the process of setting up, conducting, and reporting on the simulations underlying each SPE11 submission are at least as impactful as the computational choices reported.

Carbon capture and storage is an essential technology to mitigate anthropogenic CO2 emissions from carbon-intensive industries. To model CO2 injection, physics-based numerical methods are computationally intensive due to the nonlinear nature of the governing equations. Therefore, several data-driven deep learning methods have been developed to serve as proxies and replace numerical simulations. These proxies have demonstrated significantly faster runtimes while maintaining comparable accuracy to numerical simulations. This makes them suitable for high-fidelity models and ensemble-based techniques that require a large number of forward runs. Our method utilizes physics-informed neural networks (PINNs) to parameterize the solution space of immiscible compositional problems. The PINN parameterizes the forward solution of the compositional problem based on the composition of the upstream grid block at the updated time step, the composition of the current grid block at the current time step and the total velocity at their interface. The neural network is trained in the entire solution space and is used in a sequential, cascading solver. In this approach, we obtain the pressure solution first before solving for transport by treating the reservoir as a series of two-cell problems. The resulting transport solver is applicable to all problems with different initial/injection conditions and different heterogeneous reservoirs. We demonstrate our approach for binary and multicomponent problems and furthermore use multilinear interpolation to compare and validate the solution method.