Numerical investigation on the non-Darcy flow in fractures under the joint influence of fracture dilation and inertial effect

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.