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Transport in Porous Media

, Volume 89, Issue 1, pp 63–73 | Cite as

Capillary Pressure Curve for Liquid Menisci in a Cubic Assembly of Spherical Particles Below Irreducible Saturation

  • Jacob Bear
  • Boris Rubinstein
  • Leonid Fel
Article

Abstract

The capillary pressure–saturation relationship, P c(S w), is an essential element in modeling two-phase flow in porous media (PM). In most practical cases of interest, this relationship, for a given PM, is obtained experimentally, due to the irregular shape of the void space. We present the P c(S w) curve obtained by basic considerations, albeit for a particular class of regular PM. We analyze the characteristics of the various segments of the capillary pressure curve. The main features are the behavior of the P c(S w) curve as the wetting-fluid saturation approaches zero, and as this saturation is increased beyond a certain critical value. We show that under certain conditions (contact angle, distance between spheres, and saturation), the value of the capillary pressure may change sign.

Keywords

Porous media Two-phase flow Wetting fluid Capillary pressure curve 

List of Symbols

d

Distance between spheres

n

Number of spheres per unit cell

H

Mean curvature of meniscus

Pc

Capillary pressure

Pw, Pn

Pressures in wetting and non-wetting fluids

R

Radius of sphere

Sw, Sn

Saturations of wetting and non-wetting fluids

Swr, Snr

Irreducible w-fluid and residual n-fluid saturations

V

Volume of pendular ring

γ

Surface tension of the w–n interface

θ

Contact angle

\({\phi}\)

Porosity

ψ

Filling angle

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References

  1. Bear J., Cheng A.H.-D: Modeling Groundwater Flow and Contaminant Transport. Springer, Berlin (2010)CrossRefGoogle Scholar
  2. Brooks R.J., Corey A.T.: Hydraulic properties of porous media. Hydrology Paper 3. Colorado State University, Fort Collins (1964)Google Scholar
  3. Collins R.E.: Flow of Fluids Through Porous Materials. Reinhold Publishing Corp, New York (1961)Google Scholar
  4. Gwirtzman H., Roberts P.V.: Pore scale spatial analysis of two immiscible fluids. Water Resour. Res. 27(6), 1165–1176 (1991)CrossRefGoogle Scholar
  5. Melrose J.C.: Model calculations for capillary condensation. AIChE J. 12(5), 986–994 (1966)CrossRefGoogle Scholar
  6. Nitao J.J., Bear J.: Potentials and their role in transport in porous media. Water Resour. Res. 32(2), 225–250 (1996)CrossRefGoogle Scholar
  7. Or D., Tuller M.: Liquid retention and interfacial area in variably saturated porous media: upscaling from single-pore to sample-scale model. Water Resour. Res. 35(12), 3591–3600 (1999)CrossRefGoogle Scholar
  8. Orr F.M., Scriven L.E., Rivas A.P.: Pendular rings between solids: meniscus properties and capillary force. J. Fluid Mech. 67(4), 723–742 (1975)CrossRefGoogle Scholar
  9. Patzek T.: Verification of a complete pore network simulator of drainage and imbibition. Soc. Petrol. Eng. 71310, 144–156 (2001)Google Scholar
  10. Plateau, J.: The figures of equilibrium of a liquid mass, pp. 338–369. The Annual Report of the Smithsonian Institution, Washington, DC (1864)Google Scholar
  11. Ramirez-Flores, J.C., Bachmann, J., Marmur, A.: Direct determination of contact angles of model soils in comparison with wettability characterization by capillary rise. J. Hydrol. (2010)Google Scholar
  12. Rose W.: Volume and surface areas of pendular rings. J. Appl. Phys. 29(4), 687–691 (1958)CrossRefGoogle Scholar
  13. Rossi C., Nimmo J.R.: Modeling of water retention from saturation to oven dryness. Water Resour. Res. 30(3), 701–780 (1994)CrossRefGoogle Scholar
  14. van Genuchten M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. 44, 892–898 (1980)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Civil EngineeringTechnionHaifaIsrael
  2. 2.Stowers Institute for Medical ResearchKansas CityUSA

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