Prediction of relative permeabilities for unconsolidated soils using pore-scale network models

Pore-scale network models of two-phase capillary displacement in porous media may be used to predict constitutive relationships between the capillary pressure, saturation, and relative permeabilities at the continuum scale. Since these constitutive relationships reflect ensembles of pore-scale events, spatial correlation in the pore structure is expected to be an important consideration. Correlations in the pore structure are also evident in recent experimental studies. Pore-scale network models are used here in a quantitative investigation of the influence of correlations on the capillary pressure-saturation-relative permeability relationships. The pore space is modeled using a cubic lattice larger than 12 times the spatial correlation scale in each direction. The following two types of correlations are incorporated: spatial correlation between the radii of bonds oriented along the same direction and cross correlation between the radii of bonds emanating from the same site in all directions. Results demonstrate that the saturation-relative permeability relationship is not very sensitive to unidirectional spatial correlation but is sensitive to cross correlation. Pore-scale model parameters are fit to capillary pressure-saturation data from several real soils, followed by a prediction of the relative permeability curves for the same soils. The predicted relative permeabilities are compared to the measured values and predictions using the traditional van Genuchten relationships. The pore-scale model is shown to fit the capillary- pressure saturation curves and predict the saturation-relative permeability curves with a degree of accuracy comparable to the van Genuchten relationships. While these computations have been restricted to unconsolidated soils, they demonstrate the potential of pore-scale models for predicting other transport properties such as dispersivities and mass transfer coefficients.