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的各种不同的、可能相互竞争的应用。一方面，地下蕴藏着自然资源。另一方面，它被用来临时或永久储存废物和气体。对于所有这些相互竞争的使用类型，对我们的社会来说，评估它们的表现、局限性、风险和相互制约是不可或缺的。模型预测的质量在很大程度上取决于模型参数的质量。在这项提议中，我们主要关注地下的天然气储存，尤其是深层盐岩中的二氧化碳储存，因为我们在这一领域有很强的背景和经验。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。根据以往的研究，在模拟地下储气过程中的主要预测误差和不确定性，或者更一般地与注入流体相关的过程中的不确定性，源于地下结构和材料参数的不确定性。最近的一个例子是对德国勃兰登堡州的Ketzin试点储存场地进行建模和模拟。已经进行了一项全面的勘探和监测计划，以便根据最先进的技术提供可能的最佳数据。在这一建议的背景下，最重要的是观测数据的历史匹配，即(，)主要是在两个观测井中观测到的压力时间序列和注入二氧化碳的到达时间。模型需要具有对油藏未来动态的预测能力，并增加置信度，以便它们可以用于为注水和储存管理提供稳健的决策支持。这一建议旨在开发一种计算高效、可靠的历史拟合方法，并将其应用于地下二氧化碳储存。量化历史匹配中的不确定性和参数敏感性的方法可分为两类：(1)基于统计/随机的方法(例如，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，校准单个最优模型并提供校准后协方差的一些估计)。目前的项目将讨论这两种方法。该项目的目标是对模型校准和历史匹配中的不确定性量化的随机方法和基于优化的方法进行比较和杂交，从而结合这两个领域的最佳方面。

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.