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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

10:00 Uhr
Majid Hassanizadeh, Professor of Environmental Hydrogeology, Department of Earth Sciences, Utrecht University

150 Years of Darcy's Law - A critical look at the theories of two-phase flow in porous media

Darcy's law was proposed in 1856 to describe the flow of constant-density water in homogeneous, isotropic, non-deformable sand under isothermal conditions. Since then, that simple formula has been "extended" to be valid for flow of more fluids, with variable density, in heterogeneous, anisotropic, deformable sand under non-isothermal conditions. The extension has been achieved by adding bells and whistles to the simple equations that was proposed by Darcy.

In this presentation, we briefly describe this metamorphosis of Darcy's law and show that no real physics is actually introduced into the extended versions. In particular, we study the models of capillary effects in traditional multi-phase (and unsaturated) flow theories. Commonly, we assume that there is an algebraic relationship between capillary pressure and saturation. This relationship is based on measurements made under static conditions. This static relationship is then used to model dynamic conditions. However, it is a known fact that there is no unique relationship between capillary pressure and saturation. There are both hysteretic and non-equilibrium effects. We discuss new capillarity theories which are potentially devoid of hysteresis and include an additional term accounting for dynamic (or non-equilibrium) capillarity effects. There is compelling experimental evidence reported in the literature that the non-equilibrium effect is observable, quantifiable, and significant. In this presentation, we provide theoretical and experimental evidences of the validity of new theories. We then focus on the dynamic effect and use pore-scale and continuum scale simulation results to show the possible significance of the dynamic effect at various scales. We also investigate how the extended capillary equation affects mathematical models of unsaturated and two-phase flow models.