Fluid velocity based simulation of hydraulic fracture: a penny shaped model—part I: The numerical algorithm

Daniel Peck, Michal Wrobel, Monika Perkowska, Gennady Mishuris

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
201 Downloads (Pure)

Abstract

In the first part of this paper, a universal fluid velocity based algorithm for simulating hydraulic fracture with leak-off, previously demonstrated for the PKN and KGD models, is extended to obtain solutions for a penny-shaped crack. The numerical scheme is capable of dealing with both the viscosity and toughness dominated regimes, with the fracture being driven by a power-law fluid. The computational approach utilizes two dependent variables; the fracture aperture and the reduced fluid velocity. The latter allows for the application of a local condition of the Stefan type (the speed equation) to trace the fracture front. The obtained numerical solutions are carefully tested using various methods, and are shown to achieve a high level of accuracy.
Original languageEnglish
Pages (from-to)3615-3635
Number of pages21
JournalMeccanica
Volume53
Issue number15
Early online date22 Oct 2018
DOIs
Publication statusPublished - 01 Dec 2018

Keywords

  • Hydraulic fracture
  • Leak-off
  • Penny-shaped crack
  • Power law fluid
  • Speed equation
  • Universal algorithm

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