A model for nonlinear flow behavior in two-dimensional fracture intersections and the estimation of flow model coefficients

There are multiple flow paths with different flow directions in fracture intersections. A general flow model synthetically describing the nonlinear flow behavior of multiple flow paths in different directions in two-dimensional fracture intersections was proposed for the analysis of fluid flow in rock fracture networks. The flow behavior of seven typical fracture intersection models, according to a geological investigation, was simulated. Through numerical simulations and experimental observations, it was validated that the flow model was capable of describing the nonlinear flow behavior in each flow direction in the fracture intersections at the same time. In this flow model, the coefficient matrices include linear coefficients for each fracture branch and nonlinear coefficients for each flow path. The relations between the hydraulic pressure drops and the flow rates reflect the influence of intersection configurations and flow directions on flow behavior in the fracture intersections. Based on the flow model and corresponding non-Darcy effect factor for fracture intersections, the critical Reynolds numbers to describe the transition of the flow regime in fracture intersections were determined and found to range from 51 to 105. Furthermore, the transition of the flow regime in the fracture intersections calculated with the proposed model was found to be closely related to the evolution of microscopic flow structures in the numerical simulations.