A Continuum Approach to the Drying of Small Pore Networks

Abstract

In this chapter, the volume-averaged transport parameters of the one-dimensional macroscopic continuum model (CM) for drying are determined from two specific classes of three-dimensional microscopic discrete pore network models (PNMs) called throat-pore model (TPM) and throat-node model (TNM). The macroscopic parameters are determined for the porous microstructures corresponding to the small networks used to perform the PNM simulations. The parameters are then fed into the CM to reproduce the drying characteristics of capillary porous media. The CM is an isothermal version of the broadly accepted macroscopic CM of drying. Boundary conditions required for the solution of this CM are defined either as evaporation rate at the drying front (DF) (or at the porous medium surface) or as flux boundary conditions imposed at the interface between the gas-side boundary layer and the medium-side dry region, as well as at the interface between the dry and unsaturated regions which advances freely during drying. The CM is referred to as two-transport-zone CM when the former boundary condition is used to solve it. This CM requires the moisture transport coefficient of the porous medium as well as the relationship between saturation and relative humidity at the DF. The CM solved with the flux boundary conditions is called three-transport-zone CM, which includes three sectionally applicable transport equations. Parameters emerging in the three-transport-zone CM are the moisture transport coefficient in the wet zone within the porous medium, the vapor transport coefficient in the dry zone within the porous medium, the vapor transport coefficient in the gas-side diffusion layer, the vapor pressure–saturation relationship at the surface, as well as the vapor pressure–saturation relationship at the DF. Those macroscopic parameters are extracted from the PNM datasets after postprocessing. Since the operation of the CM is very sensitive upon the moisture transport coefficient in the totally or partially saturated zone of the porous medium, a hybrid method is introduced to control the effect of the sensitivity of the CM on the macroscopic parameters. By punctually adjusting the dataset in the high saturation period, the CM provides a stronger agreement with pore network simulations, which shows that the underlying transport phenomena are better preserved in the scattered dataset that the new hybrid method provides.