Fluid velocity based simulation of hydraulic fracture—a penny shaped model. Part II: new, accurate semi-analytical benchmarks for an impermeable solid

Daniel Peck, Michal Wrobel, Monika Perkowska, Gennady Mishuris

Research output: Contribution to journalArticlepeer-review

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Abstract

In the first part of this paper a universal fluid velocity based algorithm for simulating hydraulic fracture with leak-off was created for a penny-shaped crack. The power-law rheological model of fluid was assumed and the final scheme was capable of tackling both the viscosity and toughness dominated regimes of crack propagation. The obtained solutions were shown to achieve a high level of accuracy. In this paper simple, accurate, semi-analytical approximations of the solution are provided for the zero leak-off case, for a wide range of values of the material toughness and parameters defining the fluid rheology. A comparison with other results available in the literature is undertaken
Original languageEnglish
Pages (from-to)3637-3650
Number of pages14
JournalMeccanica
Volume53
Issue number15
Early online date24 Oct 2018
DOIs
Publication statusPublished - 01 Dec 2018

Keywords

  • Hydraulic fracture
  • Leak-off
  • Numerical solution
  • Penny-shaped crack
  • Power law fluid
  • Universal algorithm

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