A multi-flowpath model for the interpretation of immiscible displacement experiments in heterogeneous soil columns

This work focuses on the phenomenon of the immiscible two-phase flow of water and oil in saturated heterogeneous soil columns. The goal is to develop a fast and reliable method for quantifying soil heterogeneities for incorporation into the relevant capillary pressure and relative permeability functions. Such data are commonly used as input data in simulators of contaminant transport in the subsurface. Rate-controlled drainage experiments are performed on undisturbed soil columns and the transient response of the axial distribution of water saturation is determined from electrical measurements. The transient responses of the axial distribution of water saturation and total pressure drop are fitted with the multi-flowpath model (MFPM) where the pore space is regarded as a system of parallel paths of different permeability. The MFPM enables us to quantify soil heterogeneity at two scales: the micro-scale parameters describe on average the effects of pore network heterogeneities on the two-phase flow pattern; the macro-scale parameters indicate the variability of permeability at the scale of interconnected pore networks. The capillary pressure curve is consistent with that measured with mercury intrusion porosimetry over the low pressure range. The oil relative permeability increases sharply at a very low oil saturation (< 10^− 3) and tends to a high end value. The water relative permeability decreases abruptly at a low oil saturation (~ 0.1), whereas the irreducible wetting phase saturation is quite high. The foregoing characteristics of the two-phase flow properties are associated with critical (preferential) flowpaths that comprise a very small percentage of the total pore volume, control the overall hydraulic conductivity, and are consistent with the very broad range of pore-length scales usually probed in soil porous matrix.