Modeling the propagation of a hydraulic fracture is challenging due to the complex nonlinear equations and the presence of multiple scales behavior at the fracture tips. These complexities have motivated researchers to propose simplified models relying on constrained fracture geometry patterns. Amongst them, in the oil and gas industry domain, the Pseudo-3D (P3D), that computes fracture evolution in reservoirs confined by symmetric stress barriers, is frequently employed. The different assumptions made to obtain the P3D model lead to inaccurate predictions, like the overestimation of fracture height for important operating conditions. To correct such drawbacks, we propose a model discrepancy term in a multi-fidelity approach. The main difficulty associated is to construct a mapping between the inputs and outputs that faithfully represents the error between high and low fidelity models. In this paper, we investigated the efficiency modeling such discrepancy by using Gaussian processes and artificial neural networks. In this analysis, we employ three data sets with different input-output dimensions. The best model obtained is then used for carrying out an Uncertainty Quantification analysis aiming at identifying the impact of parametric uncertainty in fracture propagation computation.

中文翻译：

---

P3D液压压裂模型的数据驱动校准

由于复杂的非线性方程以及在裂缝尖端处存在多尺度行为，因此对水力裂缝的传播进行建模具有挑战性。这些复杂性促使研究人员提出了基于受约束的裂缝几何图案的简化模型。其中，在石油和天然气工业领域，经常使用伪3D（P3D）来计算受对称应力屏障限制的储层中的裂缝演化。为获得P3D模型而做出的不同假设导致了不准确的预测，例如对重要工作条件下的裂缝高度高估了。为了纠正这些缺陷，我们提出了一种多保真方法中的模型差异项。相关的主要困难是在输入和输出之间构造一个映射，以忠实地表示高保真和低保真模型之间的误差。在本文中，我们研究了使用高斯过程和人工神经网络对这种差异进行效率建模的方法。在此分析中，我们采用了三个具有不同输入输出维度的数据集。然后将获得的最佳模型用于进行不确定性量化分析，旨在确定参数不确定性对裂缝扩展计算的影响。