Summary The use of fiber optics in reservoir surveillance is bringing valuable insights into fracture geometry and fracture-hit identification, stage communication, and perforation cluster fluid distribution in many hydraulic fracturing processes. However, given the complexity associated with field data, its interpretation is a major challenge faced by engineers and geoscientists. In this work, we propose to generate distributed strain sensing (DSS)/distributed acoustic sensing (DAS) synthetic data of a crosswell fiber deployment that incorporates the physics governing hydraulic fracturing treatments. Our forward modeling can be used to add value to the interpretation task. The forward modeling is based on analytical and numerical solutions. The analytical solution is developed integrating two models: 2D fracture (e.g., Khristianovic-Geertsma-de Klerk known as KGD) and Sneddon’s induced stress. DSS is estimated using the plane strain approach that combines calculated stresses and rock properties (e.g., Young’s modulus and Poisson’s ratio). On the other hand, the numerical solution is implemented using the displacement discontinuity method (DDM), a type of boundary element method, with net pressure and/or shear stress as the boundary condition. In this case, the fiber gauge length concept is incorporated deriving displacement (i.e., DDM output) in space to obtain DSS values. In both methods, DAS is estimated by the differentiation of DSS in time. The analytical technique considers a single fracture opening and is used in a sensitivity analysis to evaluate the impact that rock/fluid parameters can promote on strain time histories. Moreover, advanced cases including multiple fractures failing in tensile or shear mode are simulated applying the numerical technique. Results indicate that our models are able to capture typical characteristics present in field data: heart-shaped pattern from a fracture approaching the fiber, stress shadow, and fracture hits. In particular, the numerical methodology captures relevant phenomenon associated with hydraulic and natural fractures interaction, which is often interpreted purely in terms of opening fractures. We can anticipate that the developed forward modeling, when embedded in a classification or regression artificial intelligence framework, will be an important tool adding substantial insights related to field fracture systems that ultimately can lead to production optimization. Also, the development of specific packages (commercial or otherwise) that explicitly model both DSS and DAS, incorporating the impact of fracture opening and slippage on strain and strain rate is still in its infancy. This paper is novel in this regard and opens up new avenues of research and applications of synthetic DAS/DSS in hydraulic fracturing processes.

中文翻译：

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通过光纤响应的分析和数值模型研究水力压裂产生的应变场

总结 光纤在储层监测中的使用为许多水力压裂过程中的裂缝几何形状和裂缝撞击识别、阶段通信和射孔簇流体分布带来了宝贵的见解。然而，鉴于与现场数据相关的复杂性，其解释是工程师和地球科学家面临的主要挑战。在这项工作中，我们建议生成井间纤维部署的分布式应变传感 (DSS)/分布式声学传感 (DAS) 合成数据，其中包含控制水力压裂处理的物理学。我们的正向建模可用于为解释任务增加价值。正演建模基于解析和数值解。分析解决方案是结合两个模型开发的：2D 断裂（例如，Khristianovic-Geertsma-de Klerk 被称为 KGD）和 Sneddon 的诱导压力。DSS 是使用平面应变方法估算的，该方法结合了计算的应力和岩石特性（例如，杨氏模量和泊松比）。另一方面，数值求解采用位移不连续法（DDM），一种边界元法，以净压力和/或剪应力为边界条件。在这种情况下，引入了光纤标距概念，在空间中导出位移（即 DDM 输出）以获得 DSS 值。在这两种方法中，DAS 都是通过 DSS 在时间上的微分来估计的。该分析技术考虑了单个裂缝开口，并用于敏感性分析，以评估岩石/流体参数对应变时程的影响。而且，应用数值技术模拟了包括在拉伸或剪切模式下失效的多个裂缝的高级案例。结果表明，我们的模型能够捕捉现场数据中存在的典型特征：接近纤维的裂缝的心形图案、应力阴影和裂缝撞击。特别是，数值方法捕捉了与水力和天然裂缝相互作用相关的相关现象，这通常纯粹根据张开裂缝来解释。我们可以预期，当嵌入分类或回归人工智能框架中时，开发的正向建模将成为一个重要的工具，增加与油田裂缝系统相关的大量洞察力，最终可以导致生产优化。还，对 DSS 和 DAS 进行明确建模的特定软件包（商业或其他）的开发，包括裂缝张开和滑移对应变和应变率的影响仍处于起步阶段。本文在这方面具有新颖性，为合成 DAS/DSS 在水力压裂过程中的研究和应用开辟了新途径。