A Fast Calculation Model for Local Head Loss of Non-Darcian Flow in Flexural Crack

Abstract

Local head loss caused by fracture intersection is often ignored because there has not been a simple method to calculate it until now. Relevant research shows that neglecting the local flow resistance leads to inaccurate results, especially when the velocity and cross angle are large. Therefore, it is necessary to find a portable method for calculation. Physical experiments of single fracture with different apertures (e = 0.77, 1.18, 1.97, 2.73 mm) were set up first to study the flow characteristics, showing obvious non-Darcian flow, which can be depicted by the Forchheimer equation when the flow velocity is sufficiently large. The computational fluid dynamics (CFD) software ANSYS FLUENT was used to build numeric simulation models. A good correlation between CFD simulation results and physical experiment results was found (Pearson's correlation coefficient > 0.99). Then, the CFD models of flexural crack with different angles from 30 • to 150 • were established to compute the pressure drop of flexural crack at different velocity. It was found that the local head loss of the flexural crack varied with the bending angle, and its coefficient was expressed by the deformation of the logistic equation. By using this model, as well as a frictional head loss equation fitted by Forchheimer equation, the head loss of crossed fissures with fixed fracture aperture could be easily calculated. Water 2020, 12, 232 2 of 15 applications, a quadratic equation (J = Av + Bv 2 ) and an exponential equation (J = Cv −m ) are used to under limited conditions [8-11]. The Forchheimer equation can express the characteristics of non-Darcian flow in fracture [12-15]: − ∇P = aQ + bQ 2 (1) where Q is volumetric flow velocity, a and b are model coefficients, and −∇P is the pressure gradient. The factors affecting the flow of fissure fluid are complex and include the shape of the fissure, degree of contact, roughness, fluid viscosity, and external pressure [16-19]. Liu et al. [20] studied the law of fluid movement in a fracture network and found that the coefficient (a, b) of the Forchheimer equation decreases with an increase in the fracture aperture, and the error in model fitting can be reduced by expressing the coefficients of the Forchheimer equation as a power equation of fracture aperture [14]. Olson et al. [21] studied the effect of the ratio of the fracture opening to its height on the flow pattern, and Shu et al. [22] studied the variation in head loss with the width of the fissure and the velocity of flow when water flows through L-shaped fissures. Li et al. [23] studied the correlation between the head loss of a fluid in cross fissures and the width as well as roughness of the fissures.This study proposes a portable calculation model where the aperture and the shape of flexural crack are considered to predict head loss directly. It is difficult to consider all factors when studying the characteristics of flow in fractures. In order to investigate the influence of each one, the synergistic effects of each condition need to be reduced, ...

Patching Hele-Shaw Cells to Investigate the Flow at Low Reynolds Number in Fracture Networks

“…Figure 7 -Geometrical representation of Model A -𝜃 = 65°When the flow has sufficiently large velocity, the flow rate can be affected intensely by intersection angle and fracture shape(Liu et al 2020), but the present results show that increasing the angle of the fractures in the linear regime of fluid flow results in negligible changes. The results of different intersection angles at the specified cross sections are presented in Figure8 and Table 4.…”