Numerical models of geothermal reservoirs typically depend on hundreds or thousands of unknown parameters, which must be estimated using sparse, noisy data. However, these models capture complex physical processes, which frequently results in long run-times and simulation failures, making the process of estimating the unknown parameters a challenging task. Conventional techniques for parameter estimation and uncertainty quantification, such as Markov chain Monte Carlo (MCMC), can require tens of thousands of simulations to provide accurate results and are therefore challenging to apply in this context. In this paper, we study the ensemble Kalman inversion (EKI) algorithm as an alternative technique for approximate parameter estimation and uncertainty quantification for geothermal reservoir models. EKI possesses several characteristics that make it well-suited to a geothermal setting; it is derivative-free, parallelisable, robust to simulation failures, and requires far fewer simulations than conventional uncertainty quantification techniques such as MCMC. We illustrate the use of EKI in a reservoir modelling context using a combination of synthetic and real-world case studies. Through these case studies, we also demonstrate how EKI can be paired with flexible parametrisation techniques capable of accurately representing prior knowledge of the characteristics of a reservoir and adhering to geological constraints, and how the algorithm can be made robust to simulation failures. Our results demonstrate that EKI provides a reliable and efficient means of obtaining accurate parameter estimates for large-scale, two-phase geothermal reservoir models, with appropriate characterisation of uncertainty.

翻译：地热储层数值模型通常依赖于数百至数千个未知参数，这些参数必须通过稀疏且含噪声的观测数据进行估计。然而，这些模型涉及复杂的物理过程，往往导致计算耗时漫长且易出现模拟失败，使得参数估计过程极具挑战性。传统的参数估计与不确定性量化方法（如马尔可夫链蒙特卡洛法）可能需要数万次模拟才能获得精确结果，因此在此类应用中难以实施。本文研究集合卡尔曼反演算法，将其作为地热储层模型近似参数估计与不确定性量化的替代技术。EKI具备多项适用于地热建模场景的特性：无需梯度计算、可并行化、对模拟失败具有鲁棒性，且所需模拟次数远少于MCMC等传统不确定性量化方法。我们通过合成案例与真实案例相结合的方式，阐释了EKI在储层建模中的具体应用。通过这些案例研究，我们进一步展示了EKI如何与灵活的参数化技术结合——这类技术既能准确表征储层特性的先验知识，又能满足地质约束条件；同时说明了算法如何实现对模拟失败的鲁棒性处理。研究结果表明，对于大规模两相地热储层模型，EKI能够在合理表征不确定性的前提下，为获取精确参数估计提供可靠高效的方法。