Dual‐porosity modelling of the pore structure and transport properties of a contaminated soil

Abstract

SummaryWe have developed a new method to characterize the pore structure of mineral soils. We combined data from the analysis of back‐scattered scanning electron microscope (BSEM) images of resin‐impregnated pore‐casts, and mercury intrusion porosimetry (MIP) data, with analytical percolation models and inverse modeling algorithms. The pore space is regarded as a dual‐pore network consisting of a primary Euclidean pore‐and‐throat network and a secondary, fractal, pore system that is accessed through primary pores. The digitized 2‐D BSEM images of resin‐impregnated soil samples are employed to determine the autocorrelation function. The Fourier transform of this function provides the small‐angle neutron scattering (SANS) intensity function, which is extended by using the surface fractal dimension obtained from high‐pressure MIP data. Inversion of the extended scattering intensity function produces the volume‐based radius distribution function of spherical pore bodies (PBRD). The complete volume‐based PBRD is fitted with a composite number‐based PBRD composed of a lognormal primary PBRD and a power (fractal) secondary PBRD with upper and lower cut‐offs. Based on the concepts of invasion percolation, an analytic mathematical model that describes Hg intrusion into dual pore networks is developed. The complete PBRD and pore‐throat radius distribution (PTRD) functions of the primary network along with the drainage accessibility functions (DAFs) of the primary and secondary pore networks are estimated with inverse modelling of the Hg intrusion curve. Based on critical path analysis of percolation theory, approximate analytical relationships are developed to calculate explicitly the absolute permeability and electrical formation factor from the geometrical and topological parameters of the primary pore network. The method is demonstrated with application to four soil samples.