Effects of velocity-dependent apparent toughness on the pre- and post-shut-in growth of a hydraulic fracture. (March 2023)

• Record Type: Journal Article
• Authors: Liu, Dong; Lu, Guanyi
• Is Part Of: Computers and geotechnics. Volume 155(2023)
• Publication Date: 2023-03
• Subjects: Hydraulic fracture -- Rate-dependent toughness -- Sub-critical fracture growth -- Gauss–Chebyshev quadrature -- Barycentric interpolations; Engineering geology -- Data processing -- Periodicals; Soil mechanics -- Data processing -- Periodicals; Rock mechanics -- Data processing -- Periodicals; 624.1510285
• DOI: 10.1016/j.compgeo.2022.105195
• Languages: English
• ISSNs: 0266-352X

Abstract

Abstract: We investigate the growth of a plane-strain/radial hydraulic fracture in an infinite impermeable medium driven by a constant injection rate assuming that the apparent toughness scales with the decreasing fracture growth rate in a power-law relation. The viscosity dominated regime always governs the fracture growth at large time for the plane-strain geometry. For a radial hydraulic fracture, we report a transition from early-time fracture growth dominated by viscous fluid flow to large-time propagation dominated by fracture toughness. Such a transition results from an overall increase of the energy dissipation by fracture surface creation. After shut-in, both plane-strain and radial fractures propagate at a lower velocity with decreasing fracture toughness. The fracture growth then depends on the dimensionless toughness at the stop of fluid injection and transitions towards a self-similar pulse-viscosity solution when viscous fluid flow dominates the energy dissipation. The fracture arrests when fulfilling two conditions — the apparent toughness reaching its minimum, and viscous forces being negligible in the fluid flow. The fracture dimension at arrest is independent of the velocity-dependent power-law relation. Highlights: Solution for hydraulic fracture growth with a power-law velocity-dependent energy. Good approximation by constant toughness solutions with instantaneous toughness. Continuous fracture propagation at a slower rate after the shut-in of fluid injection. Fracture arrests at the minimum toughness with negligible viscous forces in fluid. Pulse-viscosity solution for plane-strain hydraulic fractures.