Porous Media

Capillary saturation and desaturation

R. Hilfer, R. Armstrong, S. Berg, A. Georgiadis, H. Ott

Physical Review E 92, 063023 (2015)

submitted on
Wednesday, June 3, 2015

Capillary desaturation experiments produce disconnected (trapped) ganglia of mesoscopic sizes intermediate between pore size and system size. Experimental evidence for interactions between these mesoscale clusters during desaturation is analyzed and discussed within the established microscopic and macroscopic laws of Newton, Young-Laplace, and Darcy. A theoretical expression for capillary number correlations is introduced that seems to have remained unnoticed. It expresses capillary desaturation curves in terms of stationary capillary pressures and relative permeabilities. The theoretical expression shows that the plateau saturation in capillary desaturation curves may in general differ from the residual nonwetting saturation defined through the saturation limit of the main hysteresis loop. Hysteresis effects as well as the difference between wetting and nonwetting fluids are introduced into the analysis of capillary desaturation experiments. The article examines experiments with different desaturation protocols and discusses the existence of a mesoscopic length scale intermediate between pore scale and sample scale. The theoretical expression is derived entirely within the existing traditional theory of two-phase flow in porous media and compared to a recent experiment.

For more information see

Porous Media Two-Phase Flow

Macroscopic Equations of Motion for Two Phase Flow in Porous Media

R. Hilfer

Physical Review E 58, 2090 (1998)

submitted on
Tuesday, January 20, 1998

The usual macroscopic equations of motion for two-phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore, a more general system of macroscopic equations is derived here that incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach that exhibit a complex dependence on the state variables. A capillary pressure function can be identified in equilibrium that shows the qualitative saturation dependence known from experiment. In addition, the proposed equations include a description of the spatiotemporal changes of residual saturations during immiscible displacement.

For more information see

fluid flow Porous Media Two-Phase Flow

Old Problems and New Solutions for Multiphase Flow in Porous Media

R. Hilfer, H. Besserer

in: Porous Media: Physics, Mo\-dels, Simulation
edited by: A. Dmitrievsky and M. Panfilov
World Scientific Publ. Co., Singapore, 133-144 (2000)
ISBN: 978-981-02-4126-1

submitted on
Thursday, November 20, 1997

The existing macroscopic equations of motion for multiphase flow in porous media are unsatisfactory in two general respects. On the one hand characteristic experimental features, such as relationships between capillary pressure and saturations, cannot be predicted. On the other hand the theoretical derivation of the equations from the well-known laws of hydrodynamics has not yet been accomplished. In this paper we discuss these deficiencies and present an alternative description which is based on energy balances. Our description includes surface tensions as parameters and interface areas as a new macroscopic state variable. The equations are obtained from general multiphase mixture theory by explicitly accounting for the pairwise character of interfacial energies. For the special case of two immiscible fluids in a porous medium the most important ingredient is the distinction between a connected and a disconnected subphase of each fluid phase. In this way it becomes possible to handle also the spatiotemporal variation of residual saturations. The connection between the new approach and the established formulation is given by identifying a generalized Darcy Law with generalized relative permeabilities. The new equations reproduce qualitatively the saturation dependent behaviour of capillary pressure in gravitational equilibrium.

For more information see