HR: 16:45h
AN: H12K-04    [PDF]
TI: Soil-Moisture Retention Curves, Capillary Pressure Curves, and Mercury Porosimetry: A Theoretical and Computational Investigation of the Determination of the Geometric Properties of the Pore Space
AU: * Strand, T E
EM: tyson@geology.wisc.edu
AF: University of Wisconsin - Madison, Department of Geology and Geophysics 1215 W. Dayton St., Madison, WI 53706 United States
AU: Wang, H F
EM: wang@geology.wisc.edu
AF: University of Wisconsin - Madison, Department of Geology and Geophysics 1215 W. Dayton St., Madison, WI 53706 United States
AB: Immiscible displacement protocols have long been used to infer the geometric properties of the void space in granular porous media. The three most commonly used experimental techniques are the measurement of soil-moisture retention curves and relative permeability-capillary pressure-saturation relations, as well as mercury intrusion porosimetry experiments. A coupled theoretical and computational investigation was performed that provides insight into the limitations associated with each technique and quantifies the relationship between experimental observations and the geometric properties of the void space. It is demonstrated that the inference of the pore space geometry from both mercury porosimetry experiments and measurements of capillary pressure curves is influenced by trapping/mobilization phenomena and subject to scaling behavior. In addition, both techniques also assume that the capillary pressure at a location on the meniscus can be approximated by a pressure difference across a region or sample. For example, when performing capillary pressure measurements, the capillary pressure, taken to be the difference between the injected fluid pressure at the inlet and the defending fluid pressure at the outlet, is increased in a series of small steps and the fluid saturation is measured each time the system reaches steady. Regions of defending fluid that become entrapped by the invading fluid can be subsequently mobilized at higher flow rates (capillary pressures), contributing to a scale-dependence of the capillary pressure-saturation curve that complicates the determination of the properties of the pore space. This scale-dependence is particularly problematic for measurements performed at the core scale. Mercury porosimetry experiments are subject to similar limitations. Trapped regions of defending fluid are also present during the measurement of soil-moisture retention curves, but the effects of scaling behavior on the evaluation of the pore space properties from the immiscible displacement structure are much simpler to account for due to the control of mobilization phenomena. Some mobilization may occur due to film flow, but this can be limited by keeping time scales relatively small or exploited at longer time scales in order to quantify the rate of film flow. Computer simulations of gradient-stabilized drainage and imbibition to the (respective) equilibrium positions were performed using a pore-scale modified invasion percolation (MIP) model in order to quantify the relationship between the saturation profile and the geometric properties of the void space. These simulations are similar to the experimental measurement of soil-moisture retention curves. Results show that the equilibrium height and the width of the equilibrium fringe depend on two length scale distributions, one controlling the imbibition equilibrium structure and the other controlling the drainage structure. The equilibrium height is related to the mean value of the appropriate distribution as described by Jurin's law, and the width of the equilibrium fringe scales as a function of a combined parameter, the Bond number, Bo, divided by the coefficient of variation (cov). Simulations also demonstrate that the apparent radius distribution obtained from saturation profiles using direct inversion by Jurin's law is a subset of the actual distribution in the porous medium. The relationship between the apparent and actual radius distributions is quantified in terms of the combined parameter, Bo/cov, and the mean coordination number of the porous medium.
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3250 Fractals and multifractals
DE: 3299 General or miscellaneous
DE: 5114 Permeability and porosity
SC: Hydrology [H]
MN: 2003 Fall Meeting