Coupling flow and poromechanics simulations for geological carbon storage




Lu, Xueying, Ph. D.

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Under the framework of the Paris Agreement, achieving carbon neutrality by the middle of the century is the fundamental solution to cope with the Climate Crisis. Carbon Capture, Storage, and Usage (CCUS) is a key group of technology to achieve a net-zero energy system. A high-fidelity model that depicts the multiphysics of the carbon storage processes over multiple temporal and spatial scales is essential to predict the fate of injected CO₂ and the associated geological formation. In this dissertation, we address several computational challenges arising from high-fidelity simulations of coupling geomechanics models to the multiphase multicomponent fluid flow models for geological carbon sequestration. The necessity of the coupling is first demonstrated using field data from the Cranfield site. Numerical experiments demonstrate that coupling geomechanics enables more accurate estimation of storage volume by considering the geological formation deformation. The geomechanics simulations also depict the stress evolution in both the reservoir and caprock during the carbon storage processes, which is key to ensure caprock integrity for both short-term and long-term success of the project. However, geomechanics simulations are computationally expensive in field-scale simulations. We develop several multiscale adaptive algorithms that root on rigorous a posteriori error estimates of the Biot system solved with a fixed-stress split. Error indicators are developed using residual-based a posteriori error estimates, with theoretical guarantees. We validated the effectiveness of the error indicators with Mandel's problem and proposed novel adaptive algorithms leveraging these a posteriori error estimators. The efficiency of these error estimators to guide dynamic mesh refinement is demonstrated with a prototype unconventional reservoir model containing a fracture network. We further propose a novel stopping criterion for the fixed-stress iterations using the error indicators to balance the fixed-stress split error with the discretization errors. The new stopping criterion does not require hyperparameter tuning and demonstrates efficiency and accuracy in numerical experiments. We also formulate a three-way coupling algorithm for fluid flow models and poromechanics models. The three-way coupling uses an error indicator at each time step to determine if the mechanics equation must be solved and whether the fixed-stress iterative coupling is necessary; otherwise, only the flow equation is solved with an extrapolated mean stress. The convergence of three-way coupling is established for the single-phase flow and linear elasticity with numerical validations. We further extend the algorithm to the compositional flow model. Field scale simulations demonstrate the accuracy and efficiency of the three-way coupling algorithm in that the mechanics update time is reduced significantly compared to the standard fixed-stress split. Another attempt is to integrate Bayesian optimization into the high-fidelity simulations for carbon injection scheduling optimization. The proposed framework represents a first attempt at incorporating high-fidelity physical models and machine learning techniques for data assimilation and optimization for field-scale geological carbon sequestration applications. The high-fidelity multiphysics simulations strictly honor the physical processes during carbon sequestration, while the Bayesian optimization provides a rigorous statistical framework that balances the exploration-exploitation tradeoff, and effectively searches the surrogate solution space. A benchmark with other commonly used algorithms such as genetic algorithm and evolution strategy demonstrates a very high potential of further applications of Bayesian optimization


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