The crack tip solution for hydraulic fracturing in a permeable solid
type: Item
instance of: scholarly article
title: The crack tip solution for hydraulic fracturing in a permeable solid
zbMATH Open document ID: 0919.73254
DOI: 10.1016/0022-5096(95)00026-F
published in: Journal of the Mechanics and Physics of Solids
publication date: 1999-01-26T00:00:00Z
review text: We present self-similar analytical solutions for a hydraulically driven fracture propagating in a solid which is in a state of plane strain. In particular, we examine the effect of fluid loss on the formation modelled by the Carter leak-off mechanism. Our main new results are asymptotic solutions for arbitrary rock permeability; it is shown how these may be represented by an expansion whose leading term is the near-tip solution in the high permeability limit. Our conclusion for applications is that the solution in the practical case of intermediate permeability may be constructed as a series which starts from the loss dominated limit. We also provide a detailed comparison of our predictions with results from a numerical model which includes a fluid lag zone.
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74F10
zbMATH DE Number: 1025642
zbMATH Keywords: integrable singularity
zbMATH Keywords: self-similar analytical solutions
zbMATH Keywords: plane strain
zbMATH Keywords: effect of fluid loss
zbMATH Keywords: Carter leak-off mechanism
zbMATH Keywords: asymptotic solutions
zbMATH Keywords: near-tip solution
zbMATH Keywords: high permeability limit
zbMATH Keywords: fluid lag zone
author: B. Lenoach
MaRDI profile type: Publication
cites work: Plane strain fracture in poroelastic media
cites work: The averaging method for asymptotic evolutions. I: Stochastic differential equations
cites work: Q3714635
cites work: Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks
cites work: Q5822969
cites work: The crack tip region in hydraulic fracturing
cites work: Q5598946
full work available at URL: 0022-5096(95)00026-f
OpenAlex ID: W1985790107
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description: scientific article; zbMATH DE number 1025642