Homogenization of two-phase fluid flow in porous media via volume averaging

Jie Chen, Shuyu Sun*, Xiaoping Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A technique of local volume averaging is employed to obtain general equations which depict mass and momentum transport of incompressible two-phase flow in porous media. Starting from coupled Navier–Stokes–Cahn–Hilliard equations for incompressible two-phase fluid flow, the averaging is performed without oversimplifying either the porous media or the fluid mechanical relations. The resulting equations are Darcy's law for two-phase flow with medium parameters which could be evaluated by experiment. The Richards’ equation of the mixed form can be deduced from the resulting equations.The differences between the resulting equations and the empirical two-phase fluid flow model adopted in oil industry are discussed by several numerical examples.

Original languageEnglish (US)
Pages (from-to)265-282
Number of pages18
JournalJournal of Computational and Applied Mathematics
StatePublished - Jun 2019

Bibliographical note

Funding Information:
The work is supported by the National Natural Science Foundation of China (No.11401467), China Postdoctoral Science Foundation (No. 2013M542334. and No. 2015T81012) and Natural Science Foundation of Shaanxi Province, China (No. 2015JQ1012). S. Sun acknowledges that this work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST, Saudi Arabia through the grant BAS/1/1351-01-01.

Publisher Copyright:
© 2018 Elsevier B.V.


  • Darcy's law for two-phase flow
  • Navier–Stokes–Cahn–Hilliard equations
  • Porous media
  • Richards’ equation
  • Volume averaging

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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