The effect of micro-heterogeneity and capillary number on capillary pressure and relative permeability curves of soils

The determination of the two-phase flow coefficients (such as the capillary pressure, Pc, and relative permeabilities, krw, kro) is of a key importance to model the two-phase flow processes taking place during contaminant transport in subsurface. In the present work, transient immiscible displacement experiments are performed at various flow rates on long disturbed soil columns. The capillary pressure–saturation-relative permeability relationships of soils characterized by narrow and broad grain size distributions are estimated with inverse modeling from rate-controlled displacement experiments and are correlated with the grain size variability and ratio of viscous to capillary forces (capillary number). A soil core holder assembled with electrodes is constructed to monitor the axial distribution of water saturation. A new technique is developed to determine the water saturation averaged over successive segments of the soil column by measuring the transient responses of the electrical resistance between vertical ring electrodes. The transient responses of the average oil (water) saturation in five segments along with the total pressure drop across the soil column are introduced into an inverse modeling numerical solver of the macroscopic two-phase flow equations to estimate simultaneously the capillary pressure and relative permeability curves under dynamic conditions. The water and oil relative permeabilities increase drastically with the capillary number, while the capillary pressure curve of soils with broad grain (pore) size distribution is wider than that of soils with narrow grain (pore) size distribution. For soils with high variability of grain sizes, the irreducible wetting phase saturation is higher, the relative permeability curves are sharper and the end oil relative permeability is higher compared to soils with low variability of grain sizes.