Understanding the time-dependent behavior of reservoir and sealing formations for geologic carbon storage is critical to assessing geomechanical risks since time-dependent deformation strongly influences the mechanical response of some rock types. Many studies have evaluated the risk of CO₂ leakage and induced seismicity by assuming poroelastic rheology in sealing formations. Few have considered viscoelastic or other time-dependent responses, and much of the literature on the long-term mechanical behavior of rocks examines only a 1D uniaxial response. This is primarily because, to date, the general form of a reasonable 3D time-dependent model for rocks remains unclear. In this paper, we propose an approach to address this by using a new workflow to estimate constitutive modeling parameters for the evaluation of a 3D viscoelastic model. The proposed approach uses a 1D power-law response to extrapolate several-hour-long experimental data to the decades-long time frames of interest in geologic carbon storage. Experimental data were obtained by conducting multi-level loading/unloading triaxial relaxation tests with four different rock types. The experimental results showed that the maximum load relaxation observed is approximately 49%, with some rock types considered showing as little as 1.4%. Using the proposed workflow, two linear 3D viscoelastic models, i.e., generalized Maxwell (GM) model and fractional Kelvin-Voigt (FKV) model, were evaluated and their model parameters were chosen with the extrapolated 30-year data such that a maximum deviation from the assumed power-law response for these two 3D models was 2 MPa in axial stress and 7 MPa in radial stress. We provided reasonable ranges for the model parameters to be later used for 3D modeling of rock time-dependent responses. Our results also showed that when GM is selected to analyze the rocks considered here, the relaxation time has a general range of 1–10¹⁰ s. This time scale captures the time-dependent behavior as long as centuries, which is much longer than a 10–30 years-long time frame envisioned for CO₂ injection projects.

了解储层和封闭地层的地质碳储存随时间变化的行为对于评估地质力学风险至关重要，因为随时间变化的变形会强烈影响某些岩石类型的力学响应。许多研究评估了 CO ₂的风险通过假设密封地层中的多孔弹性流变学来研究泄漏和诱发地震活动。很少有人考虑过粘弹性或其他与时间相关的响应，而且许多关于岩石长期力学行为的文献只研究了 1D 单轴响应。这主要是因为迄今为止，合理的岩石 3D 时间相关模型的一般形式仍不清楚。在本文中，我们提出了一种解决此问题的方法，即使用新的工作流程来估计用于评估 3D 粘弹性模型的本构建模参数。所提出的方法使用一维幂律响应将数小时长的实验数据外推到地质碳储存中感兴趣的数十年时间框架。实验数据是通过对四种不同岩石类型进行多级加载/卸载三轴松弛试验获得的。实验结果表明，观察到的最大载荷松弛约为 49%，某些岩石类型仅显示 1.4%。使用建议的工作流程，评估了两个线性 3D 粘弹性模型，即广义 Maxwell (GM) 模型和分数 Kelvin-Voigt (FKV) 模型，并使用外推的 30 年数据选择它们的模型参数，以便与这两个 3D 模型的假定幂律响应是轴向应力为 2 MPa，径向应力为 7 MPa。我们为稍后用于岩石瞬态响应的 3D 建模的模型参数提供了合理的范围。¹⁰ 秒。这个时间尺度捕捉了长达数百年的时间依赖性行为，这比为 CO ₂注入项目设想的 10-30 年的时间框架要长得多。