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.

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中，孔隙异质性和惯性力对流体流动的相互影响已经受到质疑，但当惯性效应显着时，在高压梯度条件下准确预测裂缝流场仍然具有挑战性。为了应对这一挑战，我们通过在机械水平上将二次速度项引入线性流动模型（即描述压力梯度和流体通量之间的线性关系的局部三次定律）来严格推导出深度平均非线性流动模型。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模型的稳健性。我们发现，考虑到广泛的雷诺数 (0.01-167)，预测模型的平均速度相对误差 (<7%) 优于现有替代方案，这表明其在处理明显的惯性效应方面具有卓越的性能。最后，我们通过建立一个相关参数的经验函数来参数化新模型（ω ) 在模型中可测量的断裂特性（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且直接的。