Darcy Lecture

Eindhoven Multiscale Institute Colloquium
Prof. dr. Majid Hassanizadeh
Utrecht University, Department of Earth Sciences
Darcy lecture:
“Capillarity in Porous Media, on Micro- and Macroscale, Revisited”
When: 12 November 2012
14:30-15:00 Coffee
15:00-16:00 Lecture
16:00-17:00 Drinks + discussion
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.