The ability to make accurate predictions with quantified uncertainty provides a crucial foundation for the successful management of a geothermal reservoir. Conventional approaches for making predictions using geothermal reservoir models involve estimating unknown model parameters using field data, then propagating the uncertainty in these estimates through to the predictive quantities of interest. However, the unknown parameters are not always of direct interest; instead, the predictions are of primary importance. Data space inversion (DSI) is an alternative methodology that allows for the efficient estimation of predictive quantities of interest, with quantified uncertainty, that avoids the need to estimate model parameters entirely. In this paper, we evaluate the applicability of DSI to geothermal reservoir modelling. We first review the processes of model calibration, prediction and uncertainty quantification from a Bayesian perspective, and introduce data space inversion as a simple, efficient technique for approximating the posterior predictive distribution. We then apply the DSI framework to two model problems in geothermal reservoir modelling. We evaluate the accuracy and efficiency of DSI relative to other common methods for uncertainty quantification, study how the number of reservoir model simulations affects the resulting approximation to the posterior predictive distribution, and demonstrate how the framework can be enhanced through the use of suitable reparametrisations. Our results support the idea that data space inversion is a simple, robust and efficient technique for making predictions with quantified uncertainty using geothermal reservoir models, providing a useful alternative to more conventional approaches.

翻译：进行准确预测并量化不确定性，是成功管理地热储层的关键基础。使用地热储层模型进行预测的传统方法，通常涉及利用现场数据估计未知模型参数，然后将这些估计值的不确定性传递至所关注的预测量。然而，未知参数本身并非总是直接关注的对象；相反，预测结果才是首要目标。数据空间反演（DSI）是一种替代方法，它能够高效估计所关注的预测量并量化其不确定性，同时完全避免了估计模型参数的需要。本文评估了DSI在地热储层建模中的适用性。我们首先从贝叶斯视角回顾了模型校准、预测和不确定性量化的过程，并引入数据空间反演作为一种近似后验预测分布的简单高效技术。随后，我们将DSI框架应用于地热储层建模中的两个模型问题。我们评估了DSI相对于其他常见不确定性量化方法的准确性和效率，研究了储层模型模拟次数如何影响对后验预测分布的近似结果，并展示了如何通过使用合适的重参数化来增强该框架。我们的研究结果支持这一观点：数据空间反演是一种简单、稳健且高效的技术，可用于利用地热储层模型进行具有量化不确定性的预测，为传统方法提供了一个有用的替代方案。