A hybrid stochastic-deterministic model calibration method with application to subsurface CO2 storage in geological formations

工程师们越来越多地注意到自然地下非常不同的，可能是竞争性的应用。一方面，地下蕴藏着自然资源。另一方面，它用于临时或永久储存废物和气体。对于所有这些相互竞争的用途类型，我们的社会必须评估它们的性能、局限性、风险和相互限制。模型预测的质量很大程度上取决于模型参数的质量。在该提案中，我们主要关注地下天然气储存，特别是我们专注于深层盐水地层中的CO2储存，因为我们在该领域拥有强大的背景和经验。然而，我们强调，为这一工程应用领域应用和开发的方法可以直接转移到其他相关领域。从以前的研究中，它是已知的，主要的预测误差和不确定性，在模拟过程中的地下与气体存储，或更一般的注入的流体，从地下结构和材料参数的不确定性。最近的一个例子是对勃兰登堡/德国的Ketzin试验性储存地点的建模和模拟。为了根据最新技术水平提供尽可能好的数据，已经进行了全面的勘探和监测计划。（，）主要观测了两口观测威尔斯的压力时间序列和注入CO2的到达时间。模型需要对储层的未来行为具有预测能力，并具有更高的置信度，以便它们可以用于为管理注入和存储提供强大的决策支持。该建议旨在开发计算效率高且可靠的方法，用于地下CO2储存的历史匹配。量化历史匹配中的不确定性和参数敏感性的方法可以分为两类：（1）基于统计/随机的方法（例如，其中从条件分布中抽取多个样本）和（2）基于确定性优化的方法（例如，其中校准了单个最佳模型并提供了校准后协方差的一些估计）。本项目将讨论这两种方法。该项目的目标是比较和混合模型校准和历史匹配中的不确定性量化的随机和基于优化的方法，从而结合了两个世界的最佳方面。

Engineers increasingly attract notice to the natural subsurface for very different and possibly competing kinds of applications. On the one hand, the subsurface contains natural resources. On the other hand, it is used for temporary or permanent storage of waste and gas. For all of these competing use types, it is indispensable for our society to assess their performance, limitations, risks and mutual restrictions. The quality of model predictions depends strongly on the quality of the model parameters. Within this proposal, we have a major focus on gas storage in the subsurface, and in particular we focus on CO2 storage in deep saline formations since we have a strong background and experience in this field. However, we emphasize that the methods applied and developed for this field of engineering application can be transferred to other related fields in a straightforward way. From previous studies it is known that the main prediction errors and uncertainties in simulating processes in the subsurface associated with gas storage, or more general with injection of a fluid, arises from uncertainties in the subsurface structure and material parameters. A most recent example is the modelling and simulation for the Ketzin pilot storage site in the state of Brandenburg/Germany. A comprehensive exploration and monitoring program has been conducted in order to provide best possible data according to the state of the art. Most important in the context of this proposal is the history matching of the observation data, i.e.(,) mainly observed time series of pressure and the arrival time of injected CO2 in two observation wells. Models are required to have predictive power for the future behavior of the reservoirs with increased confidence so that they can be used to provide robust decision support for managing the injection and storage. This proposal aims to develop computationally efficient and reliable method for history matching with application to subsurface CO2 storage. The methods of quantifying uncertainties and parameter sensitivities in history matching can be divided into two classes: (1) statistics/stochastic-based approaches (e.g., in which multiple samples are drawn from conditional distributions) and (2) deterministic optimization-based approaches (e.g., in which a single optimal model is calibrated and some estimates of post-calibration covariance are provided). The current project will discuss both the approaches. The goal of this project is a comparison and hybridization of stochastic and optimization-based methods for uncertainty quantification in model calibration and history matching, thus combining the best aspects of both worlds.