Development of depth-averaged nonlinear flow model for fractures considering heterogeneity and significant inertial effects
Development of depth-averaged nonlinear flow model for fractures considering heterogeneity and significant inertial effects
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DOI：
10.1016/j.enggeo.2022.106849
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发表时间：
2022-09
影响因子：
7.4
通讯作者：
Lichun Wang;Lizhi Zheng;Tiejun Wang;J. Liu-zeng;X. Chen
中科院分区：
文献类型：
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作者：
Lichun Wang;Lizhi Zheng;Tiejun Wang;J. Liu-zeng;X. Chen
通过裂缝的流体流动是许多工程应用和地球物理过程的核心。尽管在过去的几十年里，人们已经探讨了孔隙非均匀性和惯性力对流体流动的相互交织的影响，但在惯性效应显着的高压梯度条件下准确预测裂缝流场仍然具有挑战性。为了解决这一挑战，我们通过将二次速度项引入线性流动模型中严格推导出深度平均非线性流动模型（即，描述压力梯度和流体通量之间的线性关系的局部立方定律）。通过六个不同粗糙度的粗糙壁裂缝的支持实验室实验和直接数值模拟进一步证实了所提出的模型的鲁棒性。我们发现，预测模型优于现有的替代品与可接受的相对误差的平均速度（<7%），考虑到广泛的雷诺数范围（0.01-167），这表明其上级性能处理明显的惯性效应。最后，我们通过建立将模型中的参数（ω）与可测量的断裂性质（即，孔径）;这使得预测模型对于预测加压工程环境中的局部速度场是可行的和直接的。
Fluid flow through fractures is central to many engineering applications and geophysical processes. Although the intertwined effects of aperture heterogeneity and inertial forces on fluid flow have been interrogated in last few decades, it remains challenging to accurately predict fracture flow field at high pressure gradient conditions when inertial effects are significant. To address this challenge, we rigorously derived a depth-averaged nonlinear flow model by introducing a quadratic velocity term into the linear flow model (i.e., Local Cubic Law that describes a linear relationship between pressure gradient and fluid flux) at the mechanistic level. The supporting laboratory experiments and direct numerical simulations through six rough-walled fractures with varying roughness further confirmed the robustness of the proposed model. We found that the predictive model outperforms existing alternatives with acceptable relative errors in mean velocity (<7%) considering a broad range of Reynolds number (0.01–167), suggesting its superior performance of handling pronounced inertial effects. Lastly, we parameterized the new model by establishing an empirical function that related parameter (ω) in the model to measurable fracture properties (i.e., aperture); this makes the predictive model viable and straightforward for predicting local velocity fields in pressurized engineered environments.