CDS&E: Collaborative Research: A Bayesian inference/prediction/control framework for optimal management of CO2 sequestration

1508713（Ghattas）/ 1507488（威尔考克斯）/ 1507009（Stadler）拟议工作的重点是整合科学计算、统计分析和数值分析方面的研究发展，为管理CO2储存提供一个通用平台。 这项工作的结果将对美国的能源生产至关重要，这是一个国家利益领域。地质碳储存面临两个主要挑战：诱发地震活动的风险，以及注入的二氧化碳泄漏到饮用水含水层。因此，注入地点的表征和CO2迁移的持续监测以及高压区域的应力变化对于最大化可储存的CO2量，同时确保储存地点的长期安全性特别重要。为了应对这些挑战，所提出的研究的总体目标是（1）通过求解未知地下性质的反问题，将井压和可用的地表变形数据集成到耦合孔隙力学模型中;（2）量化地下性质反演中的不确定性，以及（3）使用所得到的推断孔隙力学模型及其不确定性来设计用于井注入的最优控制策略，该最优控制策略在控制地震活动性的风险的同时优化储存的CO2的量。由于观测数据和模型都是不确定的，因此这种基于孔隙力学的推断/预测/控制框架必须考虑每个阶段的不确定性。然而，解决大规模PDE模型的随机逆/最优控制问题，如孔隙力学，是棘手的使用现有的方法，这遭受的“维数灾难”。“因此，建议通过开发可扩展的方法和算法来克服这些障碍，这些方法和算法利用问题结构来降低有效维度。虽然CO2封存的最终应用本身非常重要，但要开发的框架可以适用于更广泛的科学和工程问题，对于这些问题，必须从大规模不确定数据中推断出大规模不确定模型，然后用于解决不确定性下的最优决策问题。

1508713 (Ghattas) / 1507488 (Willcox)/ 1507009 (Stadler)The focus of the proposed work is on integrating research developments in scientific computing, statistical analysis, and numerical analysis to provide a common platform for managing CO2 storage. Results from this work will be important to energy production in the US, an area of National interest. Geological carbon storage faces two main challenges: the risk of inducing seismicity, and leakage of the injected CO2 into potable aquifers. The characterization of the injection site and continued monitoring of the CO2 migration as well as stress changes in the region of elevated pressure are therefore particularly important to maximize the amount of CO2 that can be stored, while ensuring the long term safety of storage sites. To address these challenges, the overall goal of the proposed research is to (1) integrate well pressure and, where available, surface deformation data into coupled poromechanics models by solving the inverse problem for unknown subsurface properties; (2) to quantify the uncertainty in the inversion for the subsurface properties, and (3) to use the resulting inferred poromechanics models together with their uncertainty to design optimal control strategies for well injection that optimize the amount of stored CO2 while controlling the risk of seismicity. It is essential that this poromechanics based inference/prediction/control framework takes into account uncertainties at every stage, since both the observational data and the models are uncertain. However, solving stochastic inverse/optimal control problems for large-scale PDE models, such as those of poromechanics, is intractable using current methods, which suffer from the "curse of dimensionality." Thus, it is proposed to overcome these barriers by developing scalable methods and algorithms that exploit the problem structure to reduce effective dimensionality. While the end application of CO2 storage is quite important in itself, the framework to be developed can be applicable to a broader set of science and engineering problems for which large-scale uncertain models must be inferred from large-scale uncertain data, and then used to solve optimal decision-making problems under uncertainty.