The Use of Projection-Based Model Order Reduction for Efficient Simulation of Subsurface Carbon Storage Via Adaptive and Non-Adaptive Sampling Techniques

Abstract Conducting a comprehensive risk and uncertainty analysis for a Geologic CO2 Storage (GCS) project typically requires simulating numerous realizations to ensure thorough coverage of expected design parameter ranges. Due to the complexity of these models and the need for long simulation periods to reach steady-state conditions and verify CO2 containment, high-performance computing (HPC) resources are commonly employed. Given the computational cost and demands, alternative innovative techniques are essential to streamline this process. In this study, we employ Projection-Based Model Order Reduction (PMOR) to evaluate the accuracy of three sampling techniques including Random, Latin Hypercube, and Greedy sampling, as compared to a High-Fidelity Model (HFM). The objective is to minimize the number of simulation runs while maintaining accuracy. The case study considers multiple simulation scenarios involving CO2 injection at varying rates and cumulative times within an aquifer, of a field characterized by two key uncertain attributes: rock permeability and rock porosity, which govern the reservoir flow and storage capacity. The HFM used is based on multiple 2D sections with 60 × 220 cell blocks from the 10th SPE Comparative Solution Project. Each cell in the model has two degrees of freedom, pressure and saturation, totaling 26,400 degrees of freedom. The HFM simulations were conducted using the open-source simulator GEOS, leveraging its subsurface flow simulation capabilities while excluding flow-poromechanics and thermal coupling. All simulations were executed on Stanford's HPC cluster. The study demonstrates that applying a linear Petrov-Galerkin method in the upper heterogeneous and isotropic layers of the model can reduce the number of degrees of freedom significantly, achieving less than 5% error with just 11 non-adaptive samples, and further reducing the required samples to five with adaptive sampling. However, the lower anisotropic layers exhibit greater geological complexity, necessitating more advanced nonlinear model order reduction methods to accurately capture their impact on reservoir characteristics. Over the years, subsurface simulation research has primarily focused on oil and gas applications, with many of these methods subsequently adapted for GCS modeling. However, the computational cost of GCS simulations has led to the adoption of probabilistic models as an alternative. However, due to the high uncertainty, large number of simulations and realizations are required for this approach. More recently, machine learning and deep learning have been explored as data-driven approaches, both physics-agnostic and physics-informed, to approximate solutions without solving the full governing equations. In contrast, this study revisits solving the governing physics, leveraging surrogate models projected onto lower-dimensional spaces to retain accuracy while achieving exceptional computational efficiency. Our findings pave the way for extending these techniques to more complex, fully coupled simulations that integrate all relevant physics governing CO2 storage.