A non-singular integral equation formulation to analyse multiscale behaviour in semi-infinite hydraulic fractures. (16th September 2015)

• Record Type: Journal Article
• Authors: Dontsov, E. V.; Peirce, A. P.
• Is Part Of: Journal of fluid mechanics. Volume 781(2015:Oct.)
• Publication Date: 2015-09-16
• Subjects: boundary layer structure, -- magma and lava flow, -- porous media; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2015.451
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : This study revisits the problem of a steadily propagating semi-infinite hydraulic fracture in which the processes of toughness-related energy release, viscous dissipation and leak-off compete on multiple length scales. This problem typically requires the solution of a system of integro-differential equations with a singular kernel, which is complicated by the need to capture extremely disparate length scales. In this study the governing equations are rewritten in the form of one non-singular integral equation. This reformulation enables the use of standard numerical techniques to capture the complete multiscale behaviour accurately and efficiently. This formulation also makes it possible to approximate the problem by a separable ordinary differential equation, whose closed-form solution captures the multiscale behaviour sufficiently accurately to be used in practical applications. We also consider a similar reformulation of the equations governing the propagation of a buoyancy-driven semi-infinite hydraulic fracture. The resulting numerical solution is able to capture the near-tip multiscale behaviour efficiently and agrees well with published solutions calculated in the large-toughness limit.