In the present paper, we propose an approach based on probabilistic learning for uncertainty quantification of the water-flooding processes in oil reservoir simulations, considering geological and economic uncertainties and multiple quantities of interest (QoIs). We employ the probabilistic learning on manifolds (PLoM) method, which has achieved success in many different applications. This methodology enables the construction of surrogate models to cope with expensive computational costs using high-fidelity simulators. It also allows the incorporation of unavoidable uncertainties, like in the porosity and permeability fields, resulting from difficulties in the characterization of the heterogenous subsurface media, or arising from economic instabilities. We are particularly interested in computing high-order statistics of the system response, which combines oil operational production and economic aspects, to evaluate risk losses. In this paper, we assess the efficacy of the PLoM stochastic surrogate through two numerical examples contemplating the above uncertainties and typical reservoir configurations.

中文翻译：

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使用概率学习方法的油藏注水计算模拟的不确定性量化

在本文中，我们提出了一种基于概率学习的方法，用于油藏模拟中注水过程的不确定性量化，同时考虑地质和经济的不确定性以及多个感兴趣的量 (QoI)。我们采用流形概率学习 (PLoM) 方法，该方法已在许多不同的应用中取得成功。这种方法使替代模型的构建能够使用高保真模拟器来应对昂贵的计算成本。它还允许纳入不可避免的不确定性，例如孔隙度和渗透率领域，这些不确定性是由于描述非均质地下介质的困难或经济不稳定引起的。我们对计算系统响应的高阶统计特别感兴趣，它结合了石油运营生产和经济方面，以评估风险损失。在本文中，我们通过考虑上述不确定性和典型储层配置的两个数值示例来评估 PLoM 随机代理的功效。