Abstract
In this chapter, the influence of heterogeneity in the air-entry pressure on the field-scale flow is examined. This issue is particularly important for media containing disconnected coarse-textured inclusions with low entry pressure embedded in a continuous fine-textured background with high entry pressure. During capillary-driven imbibition, the background material becomes water-saturated at a higher value of the capillary pressure than inclusions. The air phase loses its continuity and becomes trapped in inclusions. During drainage of fully water-saturated medium the inclusions can be drained only when the air entry pressure of the background material is exceeded. At the Darcy scale these two effects can be captured by the two-phase model, but not by the Richards equation, which does not account for air flow. However, at the field scale it is possible to represent these phenomena using either the two-phase formulation or the Richards model, on condition that the field-scale capillary and permeability functions are appropriately modified.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Braun C, Helmig R, Manthey S (2005) Macro-scale effective constitutive relationships for two phase flow processes in heterogeneous porous media with emphasis on the relative permeability-saturation relationship. J Contam Hydrol 76(1–2):47–85. doi:10.1016/j.jconhyd.2004.07.009
Eichel H, Helmig R, Neuweiler I, Cirpka O (2005) Upscaling of two-phase flow processes in porous media. In: Das D, Hassanizadeh S (ed) Upscaling multiphase flow in porous media, Springer, New York, pp 237–257
Jonoud S, Jackson M (2008) New criteria for the validity of steady-state upscaling. Transp Porous Media 71(1):53–73. doi:10.1007/s11242-007-9111-x
Mikelic A, van Duijn C, Pop I (2002) Effective equations for two-phase flow with trapping on the micro scale. SIAM J Appl Math 62(5):1531–1568. doi:10.1137/S0036139901385564
Quintard M, Whitaker S (1988) Two-phase flow in heterogeneous porous media: The method of large scale averaging. Transp Porous Media 3(4):357–413. doi:10.1007/BF00233177
Saez A, Otero C, Rusinek I (1989) The effective homogeneous behavior of heterogeneous porous media. Transp Porous Media 4(3):213–238. doi:10.1007/BF00138037
Stephen K, Pickup G, Sorbie K (2001) The local analysis of changing force balances in immiscible incompressible two-phase flow. Transp Porous Media 45(1):63–88. doi:10.1023/A:1011850618324
Szymkiewicz A, Helmig R, Kuhnke H (2011) Two-phase flow in heterogeneous porous media with non-wetting phase trapping. Transp Porous Media 86(1):27–47. doi:10.1007/s11242-010-9604-x
Szymkiewicz A, Helmig R, Neuweiler I (2012) Upscaling unsaturated flow in binary porous media with air entry pressure effects. Water Resour Res 48:W04522. doi:10.1029/2011WR010893
van Duijn C, Eichel H, Helmig R, Pop I (2007) Effective equations for two-phase flow in porous media: the effect of trapping at the micro-scale. Transp Porous Media 69(3):411–428. doi:10.1007/s11242-006-9089-9
Vasin M, Lehmann P, Kaestner A, Hassanein R, Nowak W, Helmig R, Neuweiler I (2008) Drainage in heterogeneous sand columns with different geometric structures. Adv Water Resour 31(9):1205–1220. doi:10.1016/j.advwatres.2008.01.004
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Szymkiewicz, A. (2013). Flow in Binary Media with Heterogeneous Air-Entry Pressure. In: Modelling Water Flow in Unsaturated Porous Media. GeoPlanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23559-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-23559-7_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23558-0
Online ISBN: 978-3-642-23559-7
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)