Quantitative Evaluation of the Onset and Evolution for the Non‐Darcy Behavior of the Partially Filled Rough Fracture

Abstract

The non‐Darcy flow behavior in unfilled and fully filled rough fractures has been investigated thoroughly for decades. Natural fractures usually be partially filled with porous media due to long‐term internal and external dynamic disturbances and water flow erosion. However, how to evaluate the nonlinear seepage characteristics of the partially filled rough fracture (PFRF) is never scrutinized. In the present study, 2D direct numerical simulations are conducted to investigate the non‐Darcy behavior for flow through 6 PFRF models under different filling conditions (i.e., filling degree, roughness, and hydraulic conductivity capability of the filling medium), which included coupling between the free and seepage flow in the unfilled and filled region, respectively. The results show that the critical non‐Darcy factor E = 0.02 can be used to judge the onset of the non‐Darcy regime in PFRF, which is also the critical point of eddy region (ER) volume mutation. The higher the filling degree and the weaker the hydraulic conductivity of the filled medium, the more significant the non‐Darcy behavior. Furthermore, the variation of ER volume can be divided into three stages with the increasing inertia effect, that is, stable stage (E < 0.02), slow nonlinear growth stage (0.02 ≤ E ≤ 0.1), and rapid linear growth stage (E > 0.1). In addition, a new model for quantitatively evaluating the non‐Darcy behavior of PFRF is developed via gene expression programming based on 735 simulation data set, which is further employed to establish the relationship between the friction factor.

A Novel Model of Hydraulic Aperture for Rough Single Fracture: Insights From Fluid Inertial and Fracture Geometry Effects

“…This indicates that rougher fractures with smaller b have weaker hydraulic conductivity. This conclusion has also been reported by Zhang et al (2024d). Furthermore, as the average mechanic aperture b decreases, the fractures exhibit more significant nonlinear flow characteristics.…”

“…Due to the excellent performance of the Forchheimer law in describing the nonlinear relationship between pressure gradients and flow rates (or Re) when fluid flows through porous media, fractures, or fractured porous media (Pascal & Quillian, 1980;Xing et al, 2021;Zhang et al, 2024d), it has been widely applied. Moreover, this equation has been demonstrated to apply to various flow regimes, meaning it can be used for all Re (Zhou et al, 2016).…”

“…The relationship between flow rate (or velocity) and pressure gradient exhibits nonlinearity. It is noteworthy that, to mitigate the impact of characteristic length (D) on the calculation results of the Re within the fracture, we have adopted the utilization of the unit-width flow rate (Q/w) within the fracture to characterize the product of velocity and feature length (vD), that is, vD = Q/w (Zhang et al, 2024d;Zhou et al, 2018). This nonlinearity becomes more significant with increasing inertial effects (Re) of the fluid (Konzuk & Kueper, 2004) and can typically be described by the Forchheimer equation [Equation 5]:…”