Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale

Viet T. Chau, Zdeněk P. Bažant*, Yewang Su

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1m (rather than 1m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 105-106 almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcytype water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot's two-phase medium and Terzaghi's effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model. This article is part of the themed issue 'Energy and the subsurface'.

Original languageEnglish (US)
Article number20150418
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2078
StatePublished - Oct 13 2016


  • Crack band model
  • Fracking
  • Hydraulic fracturing
  • Porous medium
  • Shale

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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