Empirical Macroscopic Model for Drying of Porous Media Based on Pore Networks and Scaling Theory

Abstract

Capillary effects as they occur on the pore scale during drying of porous media lead to the development of fractal drying fronts that cannot be described by classical continuous approaches. Recently, pore network models from hydrology and the petrol industry have been applied to drying. The possibility of studying drying front patterns depending on pore network topology and spatial distribution of pore size to investigate their influence on drying rates is very advantageous. However, the discrete approach has drawbacks when drying of larger sample sizes is of interest, because solving the mass balances for individual gas and liquid pores is very time consuming. An empirical model to overcome this size limitation was first presented in Metzger et al.^{[ 1 ]} In this, we applied the theory of scaling viscous stabilized drying fronts with capillary number and combined this theoretical physical approach with a dimensionless saturation profile obtained from 3D pore network simulations. In this article, we recall the model and complete the results for 2D networks. The resulting drying rate curves are compared to the results of both the pore network model and a receding front model with a sharp drying front.

Keywords:

• Dimensionless saturation profiles
• Invasion percolation
• Scaling law
• Stabilized drying front

Notes

^a The first runs of both 2D and 3D are as in Metzger et al.^{[ 1 ]}