Leaching and transport of radionuclides from cementitious waste forms and from waste tanks is a concern at the Savannah River Site and other Department of Energy sites. Computer models are used to predict the rate and direction for migration of these through the surrounding soil. These models commonly utilize relative permeability and capillary pressure correlations to calculate migration rates in the vadose (unsaturated) zone between the surface and the water table. The most commonly used capillary pressure models utilize two parameters to relate the pressure to the relative saturation between the wetting (liquid) and nonwetting (gas) phases. The correlation typically takes the form of a power law relation (e.g., Brooks and Corey and van Genuchten) or an exponential equation (e.g., Kosugi).
In this study, a pore saturation model is used to derive the capillary pressure as a function of a characteristic pore pressure and the wetting phase saturation. Singularity analyses of the total energies of the wetting and nonwetting phases give residual saturations for the two phases. The model includes separate pressures for imbibition and drainage to account for capillary hysteresis.
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The model successfully correlates a selected set of laboratory imbibition and drainage data for uniform grain size sand. Evaluation of the capillary pressure model is extended to correlate, somewhat less successfully, drainage and imbibition data from the U. S. Salinity Laboratoryâ??s UNSODA database for various soils.
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The capillary pressure model utilizes a single fitting parameter, a characteristic pore pressure, which can be related to a characteristic pore diameter by Darcyâ??s law. Regression of the UNSODA data shows that this pore diameter approximately equals the mean particle diameter.
