When:    12 November 2012

Where:  Ceres building, CE0.31, TU/e campus


In many soil and aquifer systems, one encounters simultaneous movements of two or more immiscible fluids. These systems are modeled using a modified form of Darcy’s law, mass or volume balance equations, and an empirical relationship between capillary pressure and saturation. In this lecture, Hassanizadeh will:

  • Explain the general understanding that capillary pressure is equal to the difference in pressures of two fluids. At microscale, this difference is given by the Young-Laplace equation, which prescribes an inverse relationship with the mean radius of curvature.
  • At macroscale, the difference in fluid pressures is assumed to be an algebraic empirical function of saturation, as mentioned above.
  • Provide a unifying approach to the theory of capillarity based on rational thermodynamics.
  • Present alternative definitions of capillary pressure on both micro- and macroscales. In particular, Hassanizadeh will make a clear distinction between capillary pressure and pressure difference of fluids.
  • Show that the difference in fluid pressures is a function of boundary conditions and dynamic properties of the system, such as flow rate or dynamic viscosities, based on theoretical, experimental, and computational results.
  • Propose that the capillary pressure must be an intrinsic property of the fluids/solid system and independent of dynamics of the system.
  • Introduce specific interfacial area (area of fluid/ fluid interfaces per unit volume of porous medium) as a new state variable to account for the fact that capillary pressure is a surface phenomenon and not a volumetric one.
  • Present theoretical, experimental, and computational evidences that show the empirical capillary pressure-saturation curve should be replaced with the capillary pressure-saturation-interfacial area surface rooted in thermodynamic theory.