Dynamics of viscous backflow from a model fracture network

Asaf Dana, Zhong Zheng, Gunnar G. Peng, Howard A. Stone, Herbert E. Huppert, Guy Z. Ramon

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Hydraulic fracturing for production of oil and gas from shale formations releases fluid waste, by-products that must be managed carefully to avoid significant harm to human health and the environment. These fluids are presumed to result from a variety of fracture relaxation processes, and are commonly referred to as 'flowback' and 'produced water', depending primarily on the time scale of their appearance. Here, a model is presented for investigating the dynamics of backflows caused by the elastic relaxation of a pre-strained medium, namely a single fracture and two model fracture network systems: A single bifurcated channel and its generalization for bifurcated fracture generations. Early-A nd late-time asymptotic solutions are obtained for the model problems and agree well with numerical solutions. In the late-time period, the fracture apertures and backflow rates exhibit a time dependence of and , respectively. In addition, the pressure distributions collapse to universal curves when scaled by the maximum pressure in the system, which we calculate as a function of . The pressure gradient along the network is steepest near the outlet while the bulk of the network serves as a 'reservoir'. Fracture networks with larger are less efficient at evicting fluids, manifested through a longer time required for a given fractional reduction of the initial volume. The developed framework may be useful for informing engineering design and environmental regulations.

Original languageEnglish (US)
Pages (from-to)828-849
Number of pages22
JournalJournal of Fluid Mechanics
StatePublished - Feb 10 2018

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • low-Reynolds-number flows
  • lubrication theory


Dive into the research topics of 'Dynamics of viscous backflow from a model fracture network'. Together they form a unique fingerprint.

Cite this