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Peridynamics and surrogate modeling of pressure-driven well stimulation
International Journal of Rock Mechanics and Mining Sciences ( IF 7.2 ) Pub Date : 2022-04-08 , DOI: 10.1016/j.ijrmms.2022.105105
D. Thomas Seidl , Dakshina M. Valiveti

In this work we use the peridynamics theory of solid mechanics to simulate fracture in an annular rock domain subject to an in-situ stress and create surrogate models that predict the area of the resulting cracks. Peridynamics is a non-local formulation of continuum mechanics that naturally accommodates material discontinuities. Furthermore, unlike other fracture modeling techniques there is no need to provide information about the crack path. We utilize the peridynamics code Peridigm and take a two-stage approach to fracture modeling. First an implicit solve is performed to compute the in-situ stress state. We then execute an explicit solve where a pressure loading designed to emulate fluid-driven hydraulic fracture is applied at the borehole and transmitted to the pre-stressed rock. We present results from polynomial and single and multi-level Gaussian process surrogate models constructed from a sampling study of the peridynamics model. The surrogates predict crack area given a measure of the in-situ stress anisotropy and rise time and amplitude of the pressure loading. These surrogates take a minuscule fraction of peridynamics model's running time to evaluate and are a step towards enabling advanced optimization and uncertainty quantification workflows that require many model evaluations.



中文翻译:

压力驱动井增产的近场动力学和替代模型

在这项工作中,我们使用固体力学的近场动力学理论来模拟受原位应力影响的环形岩石域中的断裂,并创建替代模型来预测产生的裂缝的面积。近场动力学是一种自然地适应材料不连续性的连续介质力学的非局部公式。此外,与其他断裂建模技术不同,不需要提供有关裂纹路径的信息。我们利用近场动力学代码 Peridigm 并采用两阶段方法进行断裂建模。首先执行隐式求解以计算原位应力状态。然后我们执行一个显式求解,其中设计用于模拟流体驱动水力压裂的压力载荷应用于钻孔并传递给预应力岩石。我们展示了多项式和单级和多级高斯过程代理模型的结果,这些模型由近场动力学模型的抽样研究构建而成。给定原位应力各向异性和上升时间以及压力载荷幅度的测量值,替代物可以预测裂纹面积。这些替代物只占用了近场动力学模型运行时间的一小部分来评估,并且是朝着实现需要许多模型评估的高级优化和不确定性量化工作流程迈出的一步。

更新日期:2022-04-08
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