Thursday, 18 December 2014
Luwen Zhuang1, S. Majid Hassanizadeh1, Anton Leijnse2, Martinus Van Genuchten3 and Amir Raoof1, (1)Utrecht University, Utrecht, 3584, Netherlands, (2)Wageningen University, Wageningen, Netherlands, (3)Utrecht University, Utrecht, Netherlands

Traditional extended Darcy’s law assumes that pressure gradient of each phase is the only driving force at horizontal direction, which means there should be no flow without pressure gradient. However, this is contradicted by some experimental results Hassanizadeh and Gray proposed that other driving forces must also exist based on thermodynamic approaches. This may include gradients of saturation and specific interfacial area in addition to pressure gradient.

Consider two soil samples with different initial water saturations. When they contact each other, water will start to redistribute until it reaches equilibrium. The part with higher initial saturation undergoes drainage and imbibition happens in the other part. Recent experiments have shown that the saturation discontinuity and pressure gradient will persist [2].

Generally, the approach for modeling these experimental results is to employ the standard two-phase flow model, including the continuity equation for each phase, extended Darcy’s law and the constitutive relationships for relative permeability and capillary pressure.

However, we cannot get any pressure gradients at equilibrium based on the standard model. So, we use a new numerical model, with several modifications to the traditional one:

  1. Generalized Darcy’s law replaces the extended Darcy’s law, adding the other two driving forces.

  2. Specific interfacial area is also involved in this model and a mass balance equation for it is added.

  3. Capillary pressure is assumed to depend not only on saturation, but also on the specific interfacial area.