Flow in Binary Media with Heterogeneous Air-Entry Pressure
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.
- 2.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 237–257Google Scholar
- 5.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
- 6.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
- 8.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
- 9.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
- 10.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