Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic---specifically, transversely isotropic---and closely linked to the layered composite structure at the microscale. In this work, we develop a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semi-analytical homogenization of a bi-layer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic Modified Cam-Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time-dependent borehole closure in a shale formation with different bedding plane directions.

中文翻译：

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基于层状微观结构均质化的页岩各向异性粘塑性模型

在许多地下应用中经常观察到页岩的粘塑性变形。许多研究表明，这种粘塑性行为是各向异性的——特别是横向各向同性的——并且在微观尺度上与层状复合结构密切相关。在这项工作中，我们开发了一个两尺度的页岩本构模型，其中各向异性粘塑性行为从双层微观结构的半解析均质化中自然出现。微观结构被建模为软层的复合物，代表由粘土和有机物形成的韧性基体，硬层对应于由硬矿物组成的脆性基体。这种分层的微观结构使宏观行为各向异性，即使各个层都使用各向同性本构法则建模。使用粘土和有机物含量以及蠕变幅度之间的共同相关性，我们将粘塑性改良凸轮粘土塑性模型应用于软层，同时将硬层视为线弹性材料，以最大限度地减少校准参数的数量。然后，我们描述了在标准材料更新子程序中建议模型的实现。该模型通过来自三个气页岩地层的样品的实验室蠕变数据进行了验证。我们还通过模拟具有不同层理平面方向的页岩地层中随时间变化的钻孔闭合来证明所提出模型的计算行为。同时将硬层视为线弹性材料，以尽量减少校准参数的数量。然后，我们描述了在标准材料更新子程序中建议模型的实现。该模型通过来自三个气页岩地层的样品的实验室蠕变数据进行了验证。我们还通过模拟具有不同层理平面方向的页岩地层中随时间变化的钻孔闭合来证明所提出模型的计算行为。同时将硬层视为线弹性材料，以尽量减少校准参数的数量。然后，我们描述了在标准材料更新子程序中建议模型的实现。该模型通过来自三个气页岩地层的样品的实验室蠕变数据进行了验证。我们还通过模拟具有不同层理平面方向的页岩地层中随时间变化的钻孔闭合来证明所提出模型的计算行为。