Rock fractures as the main flow channels, their morphological features, and spatial characteristics deeply influence the seepage behavior. Reservoir sandstones as a case study, four splitting groups of fractures with different roughness were scanned to get the geometric features, and then the seepage experiments were taken to analyze the relationship of the pressure gradient and flow rate , and the critical Reynolds number( ) and wall friction factor ( ) were determined to explain the translation of linear seepage to nonlinear seepage condition. Based on the scanning cloud data of different rough fractures, the fractures were reconstructed and introduced into the COMSOL Multiphysics software; a 3-dimensional seepage model for rough fractures was calibrated and simulated the seepage process and corresponding pressure distribution, and explained the asymmetry of flow velocity. And also, the seepage characteristics were researched considering aperture variation of different sample fractures; the results indicated that increasing aperture for same fracture decreased the relative roughness, the fitting coefficients by Forchheimer formula based on the data ~ decreased, and the figures about the coefficients and corresponding aperture described nonlinear condition of the above rough fractures. In addition, the expression of wall friction factor was derived, and relationship of , , and relative roughness indicated that increased with increasing fracture roughness considering the same aperture, resulting in nonlinear flow more easily, otherwise is not, showing that could be used to describe the seepage condition and corresponding turning point. Finally, it can be seen from the numerical results that the nonlinearity of fluid flow is mainly caused by the formation of eddies at fracture intersections and the critical pressure gradient decreases with increasing angle. And also, analysis about the coefficient in the Forchheimer law corresponding to fracture intersections considering the intersecting angle and surface roughness is proposed to reveal the flow nonlinearity. The above investigations give the theoretical support to understand and reveal the seepage mechanism of the rock rough fractures.

中文翻译：

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基于实验和建议的 3 维数值模拟研究通过岩石粗糙裂缝的非线性流动行为

岩石裂隙作为主要的流动通道，其形态特征和空间特征对渗流行为有着深远的影响。以油藏砂岩为例，对4组不同粗糙度的裂缝进行扫描，得到几何特征，然后进行渗流实验，分析压力梯度与流量、临界雷诺数( )和确定壁面摩擦系数 ( ) 来解释线性渗流到非线性渗流条件的转换。基于不同粗糙裂缝的扫描云数据，对裂缝进行重建并导入COMSOL Multiphysics软件；标定了粗糙裂缝的三维渗流模型并模拟了渗流过程和相应的压力分布，并解释了流速的不对称性。同时，研究了考虑不同样品裂缝孔径变化的渗流特性；结果表明，对于相同的裂缝，孔径越大，相对粗糙度越小，基于数据的Forchheimer公式拟合系数下降，系数和对应孔径的数字描述了上述粗糙裂缝的非线性条件。此外，推导了壁面摩擦系数的表达式， 、 、 和相对粗糙度的关系表明，考虑相同孔径，随着裂缝粗糙度的增加而增加，更容易导致非线性流动，否则不是，表明可以用来描述渗流状况及相应的转折点。最后，从数值结果可以看出，流体流动的非线性主要是由于在裂缝交叉处形成涡流，临界压力梯度随着角度的增加而减小。此外，还提出了考虑相交角和表面粗糙度的裂缝交叉点对应的 Forchheimer 定律中系数的分析，以揭示流动的非线性。上述研究为理解和揭示岩石粗裂隙渗流机理提供了理论支持。考虑到交叉角和表面粗糙度，提出了对 Forchheimer 定律中对应于裂缝交叉点的系数的分析，以揭示流动的非线性。上述研究为理解和揭示岩石粗裂隙渗流机理提供了理论支持。考虑到交叉角和表面粗糙度，提出了对 Forchheimer 定律中对应于裂缝交叉点的系数的分析，以揭示流动的非线性。上述研究为理解和揭示岩石粗裂隙渗流机理提供了理论支持。