Influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect on nonlinear flow behavior at single fracture intersections

- Flow test and numerical simulation solving NS equations on crossed fractures are conducted.
- An expression for predicting hydraulic aperture of each segment of an intersection is proposed.
- Influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect are systematically investigated.
- A necessary condition to apply the cubic law to flow through fracture intersections is suggested.

SummaryFluid flow tests were conducted on two crossed fracture models for which the geometries of fracture segments and intersections were measured by utilizing a visualization technique using a CCD (charged coupled device) camera. Numerical simulations by solving the Navier-Stokes equations were performed to characterize the fluid flow at fracture intersections. The roles of hydraulic gradient, surface roughness, intersecting angle, and scale effect in the nonlinear fluid flow behavior through single fracture intersections were investigated. The simulation results of flow rate agreed well with the experimental results for both models. The experimental and simulation results showed that with the increment of the hydraulic gradient, the ratio of the flow rate to the hydraulic gradient, Q/J, decreases and the relative difference of Q/J between the calculation results employing the Navier-Stokes equations and the cubic law, δ, increases. When taking into account the fracture surface roughness quantified by Z2 ranging 0-0.42 for J = 1, the value of δ would increase by 0-10.3%. The influences of the intersecting angle on the normalized flow rate that represents the ratio of the flow rate in a segment to the total flow rate, Ra, and the ratio of the hydraulic aperture to the mechanical aperture, e/E, are negligible when J < 10−3, whereas their values change significantly when J > 10−2. Based on the regression analysis on simulation results, a mathematical expression was proposed to quantify e/E, involving variables of J and Rr, where Rr is the radius of truncating circles centered at an intersection. For E/Rr > 10−2, e/E varies significantly and the scale of model has large impacts on the nonlinear flow behavior through intersections, while for E/Rr < 10−3, the scale effect is negligibly small. Finally, a necessary condition to apply the cubic law to fluid flow through fracture intersections is suggested as J < 10−3, E/Rr < 10−3, and Z2 = 0.