A new perspective on nonlinear flow evolution: The inference of the ideal curve and the establishment of the process hydraulic aperture

Nonlinear flow in rock fractures is often described by the Forchheimer equation; however, there are still flaws and contradictions in the understanding of the Forchheimer equation and nonlinear evolution mechanisms, such as differing interpretations of various hydraulic apertures and the factors affecting the linear and nonlinear coefficients. This study utilizes wavelet analysis filtering and reconstruction techniques to investigate the impact of roughness at different scales on nonlinear seepage. It further provides new insights into the Forchheimer equation and hydraulic aperture by introducing the concepts of the ideal curve, the ideal Reynolds number, and process hydraulic aperture, along with the proposed criteria for determining them. A new mathematical model, incorporating geometric characteristics and Reynolds number effects, is developed and validated, effectively describing hydraulic aperture variations during nonlinear flow. The findings clarify the evolution of hydraulic aperture and flow coefficients, resolve previous contradictions, and advance understanding of nonlinear seepage mechanisms.