From micro-scale to macro-scale modeling of solute transport in drying capillary porous media

Abstract

Drying of capillary porous media initially saturated with saline water is central to many engineering and environmental applications. In order to predict the evolution of solute concentration in a porous medium, the macroscopic continuum models (CMs) are commonly employed. However, the predictive aptitudes of the CMs have been questioned. In this work, we solve the classical advection-diffusion equation for solute transport in an isothermally drying capillary porous medium for the limiting condition of capillary-dominated regime. The solution of the continuum model is compared with pore network simulations. The results of both models are analyzed in terms of local solute concentration profiles for different values of network saturation. On this basis, the ability of the continuum model to reciprocate the pore network results is assessed. The degree of heterogeneity in the liquid phase structure is characterized by performing pore network Monte Carlo simulations distinguishing the percolating liquid cluster from the non-percolating isolated clusters. Based on the statistical analysis of Monte Carlo simulations, the probability of first solid crystals to appear in the respective liquid phase elements is discussed. We observe that solute enrichment is more pronounced in the isolated single liquid throats and isolated clusters due to lack or significant hindrance to back-diffusion as a result of discontinuity in the liquid phase.