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Transport in Porous Media

, Volume 86, Issue 1, pp 243–259 | Cite as

Two-Phase Flow in Porous Media: Predicting Its Dependence on Capillary Number and Viscosity Ratio

  • M. FererEmail author
  • Shelley L. Anna
  • Paul Tortora
  • J. R. Kadambi
  • M. Oliver
  • Grant S. Bromhal
  • Duane H. Smith
Article

Abstract

Motivated by the need to determine the dependencies of two-phase flow in a wide range of applications from carbon dioxide sequestration to enhanced oil recovery, we have developed a standard two-dimensional, pore-level model of immiscible drainage, incorporating viscous and capillary effects. This model has been validated through comparison with several experiments. For a range of stable viscosity ratios (M = μ injected,nwf/μ defending, wf ≥ 1), we had increased the capillary number, N c and studied the way in which the flows deviate from fractal capillary fingering at a characteristic time and become compact for realistic capillary numbers. This crossover has enabled predictions for the dependence of the flow behavior upon capillary number and viscosity ratio. Our results for the crossover agreed with earlier theoretical predictions, including the universality of the leading power-law indicating its independence of details of the porous medium structure. In this article, we have observed a similar crossover from initial fractal viscous fingering (FVF) to compact flow, for large capillary numbers and unstable viscosity ratios M < 1. In this case, we increased the viscosity ratio from infinitesimal values, and studied the way in which the flows deviate from FVF at a characteristic time and become compact for non-zero viscosity ratios. This crossover has been studied using both our pore-level model and micro-fluidic flow-cell experiments. The same characteristic time, τ = 1/M 0.7, satisfactorily describes both the pore-level results for a range of large capillary numbers and the micro-fluidic flow cell results. This crossover should lead to predictions similar to those mentioned above.

Keywords

Pore-level modeling Drainage Micro-fluidics Viscosity ratios 

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Copyright information

© US Government 2010

Authors and Affiliations

  • M. Ferer
    • 1
    • 2
    Email author
  • Shelley L. Anna
    • 1
    • 3
  • Paul Tortora
    • 1
    • 3
  • J. R. Kadambi
    • 4
  • M. Oliver
    • 4
  • Grant S. Bromhal
    • 1
  • Duane H. Smith
    • 1
    • 2
  1. 1.US DOE, National Energy Technology LaboratoryMorgantownUSA
  2. 2.Department of PhysicsWest Virginia UniversityMorgantownUSA
  3. 3.Departments of Mechanical and Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA
  4. 4.Department of Mechanical and Aerospace EngineeringCase Western Reserve UniversityClevelandUSA

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