流体惯性效应和裂隙几何属性对非达西系数的影响

文章采用数值模拟方法探究流体惯性效应和裂隙几何属性对非达西系数 $ \beta $ 的影响, 结果表明, 随着流体惯性效应 (用非达西效应因子 E 量化) 增加, $ \beta $ 减小 $ 1 \sim 2 $ 个数量级。当 $ 0 < E \leqslant 0.5 $ 时, $ \beta $ 量化模型 ( $ \beta = A e_{h}^{-2b} $) 的幂指数 -2b 和比例因子 A 受到流体惯性效应和裂隙几何属性的耦合影响, 即流体惯性效应增大会导致幂指数增大, 比例因子减小; 裂隙粗糙度增加会导致幂指数减小, 比例因子增大。当 $ 0.5 < E \leqslant 1.0 $ 时, 幂指数和比例因子的变化趋势更为复杂, 这是由于强惯性流的出现引起高异质性裂隙流场的结果。结合比例因子和幂指数的无量纲分析, 得到考虑裂隙几何属性和流体惯性效应耦合影响下的 $ \beta $ 量化模型。研究结果可为探究岩石裂隙中的非达西流提供参考。

The influence of the fluid inertia effect on the non-Darcy coefficient( $ \beta $) was numerically investigated and the influence of fracture geometric properties was also combined to quantify $ \beta $. Results showed that the $ \beta $ experienced a reduction of 1-2 orders of magnitude with the increasing fluid inertia effect (the effect was quantified by the non-Darcy effect factor E). When $ 0 < E \leq 0.5 $, the power exponent $ (-2b) $ and scaling factor (A) of the $ \beta $ quantitative model ( $ \beta = A e_{h}^{-2b} $) were affected by the coupling effect of the fluid inertia effect and fracture geometric properties. The increasing inertia effect of fluid flow could induce the increase of power exponent and the reduction of scaling factor. And the increase of fracture roughness led to the decrease of power exponent and the increase of scaling factor. When $ 0.5 < E \leq 1.0 $, the varying trend of power exponent and scaling factor was complex, which might be due to the highly heterogeneous flow field induced by strong inertial flow. Moreover, combined with the dimensionless analysis of the scaling factor and power exponent, an empirical quantitative model of the $ \beta $ considering the coupling effect of the fracture geometric properties and fluid inertia effect was obtained. The results can provide reference for exploring non-Darcy flow in rock fractures.