Numerical investigation on the non-Darcy flow in fractures under the joint influence of fracture dilation and inertial effect
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摘要:
裂隙渗流是核废料、CO2地质储存等重大工程的关键因素，常涉及高压环境。随着水力梯度增加，惯性效应增强，导致非达西效应（表观渗透率减少）。然而，前人研究常忽略高压下水力耦合作用对裂隙的扩张及相应的表观渗透率上升效应，造成刻画和模拟渗流过程不准确。为此，基于二维粗糙单裂隙和裂隙-基质系统，采用直接数值模拟方法研究裂隙扩张和惯性效应2种机制共同作用下的非达西渗流发展规律，探讨不同岩石基质力学性质对裂隙非达西渗流的影响。结果表明：（1）当压力梯度较小时，渗流处于达西流态，2种机制对渗流的影响都可以忽略，随着压力梯度逐渐升高，渗流进入非达西流态，2种机制都起到重要作用；（2）在2种机制竞争作用下，非达西渗流由惯性效应主导转向裂隙扩张主导，与之对应，裂隙等效水力开度呈现出先减小后增大的规律；（3）基质岩石的抗变形能力越弱，裂隙扩张主导效应越显著，并且使得由惯性效应转向裂隙扩张作用主导的临界值也越小，反之惯性效应主导显著。研究成果能为准确研判高压环境下裂隙介质中后达西渗流机制提供科学依据。
Abstract:The fluid flow in fractures is crucial for major engineering projects such as nuclear waste disposal and CO2 geological storage, which often involve with high-pressure environments. Previous studies have revealed that as hydraulic gradients increase, inertial effects become stronger, leading to non-Darcy effects (i.e., reduced equivalent permeability). Unfortunately, past studies often neglected the influence of hydromechanical coupling on modifying fracture morphology. This oversight leads to a failure in capturing the effects of pressure-induced dilation and the consequent increase in equivalent permeability, resulting in inaccuracies in characterizing fluid flow in fractures. To this end, this study, based on two-dimensional rough single fractures and fracture-matrix systems, used direct numerical simulation methods to investigate the joint effects of two mechanisms: fracture dilation and inertial effects on the development of non-Darcy flow, and explored the influence of different mechanical properties of rock matrix on non-Darcy flow in fractures. The study leads to following key findings: (1) when the pressure gradient is small, the fluid flow is in Darcy flow regime, and the effects of both mechanisms on fluid flow can be ignored. As pressure gradient gradually increases, the non-Darcy flow regime emerges, where both mechanisms play important roles. (2) Under the joint effects of above two mechanisms, non-Darcy regime can be further divided into two phases: inertial effect domination and fracture dilation domination. Correspondingly, the equivalent hydraulic aperture decreases first and then increases. (3) Moreover, the weaker the deformation resistance of the matrix rock, the more significant the dominant effect of fracture dilation, and the smaller the critical value at which the transition from inertial effect to fracture dilation occurs. Conversely, inertial effects dominate significantly. The findings of this study can provide a scientific basis for accurately assessing fluid flow in fractured media in high-pressure environments, ultimately helping better design and manage major engineering projects.
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表 1 基质岩性的力学性质
Table 1. List of the mechanical properties of five typical types of rock matrix
页岩 砂岩 石灰岩 花岗岩 玄武岩 杨氏模量/GPa 15 35 45 60 70 泊松比 0.15 0.22 0.28 0.25 0.25 
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表 2 不同岩性Forchheimer方程拟合参数
Table 2. Summary of Forchheimer equation fitting parameters for different types of rock matrix
参数 页岩 砂岩 灰岩 花岗岩 玄武岩 无基质 A/（1010 kg·m−5·s−1） 4.88 4.88 4.88 4.88 4.89 4.96 B/（1013 kg·m−8） 6.09 7.59 7.99 8.13 8.23 8.24 R2 0.99 0.99 0.99 0.98 0.96 0.98
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