Non-local equilibrium continuum modeling of partially saturated drying porous media: Comparison with pore network simulations

Abstract

A two equation continuum model is developed to simulate the mass transfer in drying porous media. The main goal is to capture the so called non equilibrium effect To this end , we opera te in a regime where the liquid phase is immobile so that non equilibrium mass exchange between liquid and vapor phase dom inates. The formulation of the model relies on an upscaling technique. This notably permits to formula te the non local equilibrium phase change term on a firmer basis. The upscaling also indicates that there is no reason to consider an enhancement factor in the vapor diffusion model. The macroscopic model parameters are determined from pore network drying simulations. The same simulations are also used as a reference to compare with the predictions of the non local equilibrium continuum model. The solu tion of the two equation continuum model proves that this model simulates the non local equilibrium effect with reasonable accuracy. Also, the simulations indicate that the non local equilibrium effect is especially significant at the porous medium surface.

Coupling between internal and external mass transfer during stage-1 evaporation in capillary porous media: Interfacial resistance approach

“…As in many previous works, e.g. [7,10,11,13,16,17,18], a simple cubic network is considered (Fig. 2).…”

“…The computation of saturation profiles from PNM simulations requires defining an averaging volume (AV). As in several previous works [7,11,13,16], horizontal slices of thickness a (where a is the lattice spacing) are considered. Each slice contains N × N pore bodies located in a horizontal plane and the half of the vertical throats connecting the slice pore bodies to the pore bodies in the two adjacent horizontal planes.…”

“…However, an alternative is to proceed via comparisons with macroscopic data obtained from pore scale numerical simulations. This latter approach has notably been developed using pore network model (PNM) simulations [7,[10][11][12][13]. Naturally, it is then expected that the PNM simulations are "sufficiently" representative of the drying process for the comparison between the continuum models and the PNM simulations to be also insightful as regards the performance of the continuum models with respect to the experiments.…”

Percolating and nonpercolating liquid phase continuum model of drying in capillary porous media with application to solute transport in the very low Péclet number limit

“…With our definitions, the microscopically percolating liquid region corresponds to the main cluster whereas the isolated clusters correspond to the microscopically non-percolating regions. As in a series of previous works [13,19,20,21], the method to discuss the relevance of the continuum model is to proceed via comparisons with simulations with a pore network model (PNM) of drying. However, since PNMs have been developed and a PNM is used here as a reference, one can wonder why continuum models are still worth of interest.…”

The Brooks and Corey Capillary Pressure Model Revisited from Pore Network Simulations of Capillarity-Controlled Invasion Percolation Process

“…In pore network modeling, the void space of a porous medium is approximated by a network of connected throats and pores (herein called throat-pore model, TPM) and transport phenomena are described by unidirectional approximations at the level of individual throats and pores. Uses of PNMs for the computation of macroscopic parameters (such as permeability, relative permeability and capillary pressure curve) have already been elucidated in numerous previous studies (e.g., [20][21][22][23]) as well as in recent literature (e.g., [4,[24][25][26][27][28]). Nevertheless, none of those works have systematically investigated the impact of pore structure on the Brooks and Corey capillary pressure model parameters.…”