地质构造中$CO_2$存储的概率建模和全局敏感性分析：谱方法
Probabilistic modeling and global sensitivity analysis for $CO_2$ storage in geological formations: a spectral approach
摘要：
这项工作的重点是模拟$CO_2$存储在地下深处地层的不确定性，并试图了解储层性质的不确定性对$CO_2$泄漏的影响。为了模拟该过程，使用具有平衡相交换的非等温两相两组分流动系统。由于模型评估是计算密集型的，而不是传统的蒙特卡罗方法，我们依赖于多项式混沌（PC）的扩展表示的随机模型响应。一个非侵入性的方法是用来确定PC系数。我们通过系统的收敛性研究，在合理的误差阈值内建立PC表示的准确性。除了表征模型观测量的分布，我们计算过量$CO_2$泄漏的概率。此外，我们认为注入率作为一个设计参数，并计算出最佳的注入率，以确保在泄漏井的超压建设的风险保持在可接受的水平以下。我们还提供了一个全面的分析灵敏度的$CO_2$泄漏，我们计算的贡献的随机参数，以及它们的相互作用，通过计算第一，第二，和总阶Sobol指数的方差。
英文摘要：
This work focuses on the simulation of $CO_2$ storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on $CO_2$ leakage. To simulate the process, a non-isothermal two-phase two-component flow system with equilibrium phase exchange is used. Since model evaluations are computationally intensive, instead of traditional Monte Carlo methods, we rely on polynomial chaos (PC) expansions for representation of the stochastic model response. A non-intrusive approach is used to determine the PC coefficients. We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies. In addition to characterizing the distributions of model observables, we compute probabilities of excess $CO_2$ leakage. Moreover, we consider the injection rate as a design parameter and compute an optimum injection rate that ensures that the risk of excess pressure buildup at the leaky well remains below acceptable levels. We also provide a comprehensive analysis of sensitivities of $CO_2$ leakage, where we compute the contributions of the random parameters, and their interactions, to the variance by computing first, second, and total order Sobol' indices.
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