Pore saturation model for capillary imbibition and drainage pressures

Background

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 or an exponential equation.

Results

A pore saturation model is used to derive the secondary drainage pressure and the bounding imbibition pressure as functions of a characteristic pore pressure and the liquid saturation. The model utilizes singularity analyses of the total energies of the liquid and gas to obtain residual saturations for the two phases.

Conclusions

The model successfully correlates a selected set of laboratory imbibition and drainage data for sand. The capillary pressure model utilizes a single fitting parameter, a characteristic pore pressure, which is related to a characteristic pore diameter by the Laplace equation. This pore diameter approximately equals the diameters predicted by two different geometric pore models based on the particle diameter.