# 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

Abstract:

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.

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

Abstract:

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.