2014/04/16 by A. M. Linkov, Aleksandr M. Linkov, Linkov, Aleksandr M.
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics (physics.geo-ph) #Hydraulic Fracturing and Reservoir Analysis #Reservoir Engineering and Simulation Methods #Seismic Imaging and Inversion Techniques #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.1404.4165
11 pages
arxiv created 2014/04/16 · openalex publication_date 2014/04/16 · arxiv updated 2014/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.